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ELECTRICITY  AND  MAGNETISM 

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iii 


:iH'^']L 


iv  PREFACE 

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PREFACE  V 

maximum  of  information  in  a  minimum  space,  but  this 
information  is  so  ingeniously  arranged  and  correlated,  and 
the  indexes  are  so  full  and  complete,  that  it  can  at  once  be 
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when  it  should  be  used. 

This  volume  treats  of  the  elements  of  electricity  and 
magnetism,  including  a  detailed  description  of  primary  and 
secondary  batteries,  and  a  full  and  complete  discussion  of 
the  physical  theory  of  the  dynamo.  As  the  subject  matter 
here  presented  forms  the  groundwork  of  electrical  engineer- 
ing, every  effort  has  been  made  to  bring  out  those  points 
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of  numerous  examples  and  illustrations.  The  various  elec- 
trical measurements  have  been  given  in  an  unusually  clear 
manner,  so  that  they  can  readily  be  understood  and  applied 
to  every-day  wOrk,  even  by  those  who  are  not  accustomed 
to  making  such  measurements.  Special  attention  has  been 
paid  to  storage  batteries,  owing  to  their  large  and  increasing 
use  in  connection  with  central  stations,  and  primary  bat- 
teries have  been  described  much  more  fully  than  in  ordinary 
textbooks.  Besides  being  of  great  value  to  those  making  a 
specialty  of  electrical  work,  this  volume  will  be  found  an 
excellent  textbook  by  persons  connected  with  electrical 
enterprises  who  wish  to  gain  a  general  knowledge  of  elec- 
tricity and  magnetism. 

As  mentioned  above,  this  volume  is  printed  from  the 
plates  used  in  printing  the  Reference  Libraries  of  the  Inter- 
national Correspondence  Schools.  On  account  of  the  omis- 
sion of  certain  papers,  the  material  contained  in  which  is 
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the  volume,  as  the  index  has  been  reprinted  and  made  to 
conform  to  the  present  arrangement. 

International  Textbook  Company. 


CONTENTS. 


Principles  op  Electricity  and  Magnetism.  Page. 

Introductory          .......  1449 

Electrostatics         -         -         -         -         -         -         -  1450 

Electrostatic  Induction          -         .         .         .         .  1456 

Electrodynamics -  1463 

Circuits          -         -         -         -         -         -         -         -  1471 

Electrical  Units    -------  1472 

Ohm's  Law  Applied  to  Closed  Circuits          -         -  1491 

Ohm's  Law  Applied  to  Derived  Circuits      -          -  1500 

Magnetism    --------  1517 

Magnetic  Lines  of  Force       -----  1520 

Magnetic  Induction      -         -         -         -         -         -  1524 

Electromagnetism          ------  1528 

Electrical  Apparatus  and  Experiments         -         -  1530 

Electromagnetic  Reaction    -----  1541 

The  Electromagnet       ------  1546 

Magnetizing  Force  and  Magnetic  Density  -         -  1550 

Lifting  Magnets   -------  1568 

Magnets  for  Attraction         .         -         .         -         -  1576 

Electromagnetic  Induction  -----  1579 

Electrical  Measurements. 

Electromagnetic  Measurements    -         -         -         -  1591 

Theory  of  the  Galvanometer         -         -         -         -  1592 

Galvanometer  Shunts   ------  1620 

Precision  in  Measurements   -----  1623 

Electrochemical  Measurements    .         -         -         -  1625 

Measurement  of  Potential    -----  1632 

vii 


viii  CONTENTS. 

Electrical  Measurements — Continued.  Page. 

Measurement  of  Resistance  -----  1635 

Temperature  Coefficient        -----  1646 

Insulation      --------  1649 

Electrical  Apparatus     ------  1659 

Practical  Measurements         .         _         -         -         -  1670 

Instruments  --------  1670 

Measurements  with  Commercial  Instruments       -  1682 

Batteries. 

Definitions    --------  1689 

Principles  of  Chemistry          .          -         -         -         .  1690 

Electrochemistry  -------  1699 

Polarization  and  Depolarization    -         -         -         -  1709 

Cells      ---------  1712 

Cells  with  a  Non-Depolarizing  Electrolyte  -         -  1714 

Cells  with  a  Depolarizing  Electrolyte  -          -          -  1718 

Cells  with  a  Liquid  Depolarizer    -         -         -         -  1723 

Cells  with  a  Solid  Depolarizer       -         -         -         -  1739 

Cells    in    Which    an     Elementary     Substance    is 

Applied  to  the  Cathode  as  a  Depolarizer        -  1750 

Dry  Batteries        -------  1751 

Application  of  Primary  Batteries           -          -          -  1752 

Accumulators        -------  1759 

Uses  of  Accumulators  ------  1781 

Installation  of  Accumulators        -         -         -     .    -  1791 

Applied  Electricity. 

Theory  of  Dynamo        -          -          -          -          -         -  1897 

Generation  of  E.  M.  F.          -         -         -         -         -  1899 

Graphical  Representation  of  E.  M.  F.  or  Current  1911 

The  Air-Gap          -------  1922 

Armature  Core  Losses  ------  1924 

Character  of  Commercial  Currents       -         -         -  1927 

General  Principles  of  Armature  Windings    -         -  1929 

Open-Coil  Bipolar  Armatures        -         -         -         -  1938 

Dpen-Coil  Multipolar  Armatures           -         -         -  1950 

Closed-Coil  Bipolar  Armatures      -         -         -         -  1954" 

Closed-Coil  Armature  Windings  -         -         -         -  1973 


CONTENTS.  ix 

Applied  Electricity — Continued.  Page. 

Ring  Windings      ---....  1974 

Bipolar  Drum  AVindings        -         .         -         .         .  1982 

Multipolar  Drum  Windings           -         -        '-         -  1994 

Multiple  Windings         ---...  2002 

The  Magnetic  Circuit   ------  2017 

Construction  of  Frame           -         -         .         -         .  2018 

Form  of  Magnetic  Circuit     -----  2021 

Methods  of' Exciting  the  Field      -         -         .         -  2029 


PRINCIPLES  OF  ELECTRICITY  AND 
MAGNETISM. 


INTRODUCTORY. 

2201.  Electricity  is  the  name  given  to  that  which 
directly  causes  all  electrical  phenomena.  The  word  is 
derived  from  the  Greek  word  clektron,  meaning  amber. 

Although  electrical  science  has  made  great  advances  in 
the  last  few  years,  the  exact  nature  of  electricity  is  un- 
known. Recent  researches  tend  to  demonstrate  that  all 
electrical pheno77tena  are  due  to  a  peculiar  state  or  stress  of  a 
medium,  called  ether  (see  Art.  1 1 26) ;  that,  when  in  this 
condition,  the  ether  yoss&ss&s  potential  energy  ov  capacity  for 
doing  zuork,  as  is  manifested  by  attractions  and  repulsions, 
by  chemical  decomposition,  and  by  luminous,  heating,  and 
various  other  effects. 

2202.  All  researches  tend  to  prove  that  electricity  is 
not  a  form  of  matter,  for  the  only  physical  properties  it 
possesses  in  common  with  material  substances  are  indestruc- 
tibility and  elasticity;  it  does  not  possess  tveight,  extension, 
nor  any  of  the  other  physical  properties  of  matter. 

2203.  Electrical  science  is  founded  upon  the  effects 
produced  by  tJie  action  of  certain  forces  upon  matter,  and  all 
knowledge  of  the  science  is  deduced  from  these  effects. 
The  study  of  the  fundamental  principles  of  the  science  is  an 
analysis  of  a  series  of  experiments  and  the  classification  of 
the  results,  under  laws  and  rules.  It  is  not  necessary  to 
keep  in  mind  any  hypothesis  as  to  the  exact  nature  of  elec- 
tricity;   its  effects  and  the  laws  which    govern  them   are 

For  notice  of  the  copyright,  see  page  immediately  following  th«  title  page. 


1450 


PRINCIPLES  OF 


quite  similar  to  those  of  well-known  mechanical  and  natural 
phenomena,  and  will  be  best  understood  by  comparison. 

2204.  Electricity  may  appear  either  to  reside  upon  the 
surfaces  of  bodies  as  a  charge^  under  high  pressure,  or  flow 
through  their  substance  as  a  current^  under  comparatively 
low  pressure. 

That  branch  of  the  science  which  treats  of  charges  upon 
the  surfaces  of  bodies  is  termed  electrostatics,  and  the 
charges  are  said  to  be  static  charges. 

Electrodynamics  is  that  branch  which  treats  of  the 
action  of  electric  currents. 


ELECTROSTATICS. 


PRODUCTION  OF  STATIC  ELECTRICITY. 
2205.  When  a  glass  rod  or  a  piece  of  amber  is  rubbed 
with  a  piece  of  silk  or  fur,  the  parts  rubbed  will  be  found  to 
have  the  property  of  attracting  light  bodies,  such  as  pieces 
of  silk,  wool,  feathers,  gold-leaf,  pith,  etc.,  which,  after 
momentary  contact,  are  again  repelled.  These  attractions 
and  repulsions  are  caused  by  a  static  charge  of  electricity 
residing  upon  the  surfaces  of  those  bodies.  A  body  in  this 
condition  is  said  to  be  electrified. 

A  better  experiment  for  demonstrating  this  action  is  to 
suspend  a  small  pith-ball  by  a  silk  thread  from  a  support  or 

bracket,  as  shown  in  Fig.  901. 
Such  an  apparatus  is  spoken  of  as 
an  electric  pendulum.  If  a 
static  charge  of  electricity  be 
developed  on  a  glass  rod  by  rub- 
bing it  with  silk,  and  the  rod  be 
brought  near  the  pendulum,  the 
ball  will  be  attracted  to  the  rod, 
but  after  momentary  contact  will 
be  repelled.  By  this  contact  the 
ball  becomes  electrified,  and  so 
pjq  901.  \ov\^  as  the  two  bodies  retain  their 


ELECTRICITY  AND  MAGNETISM.  1451 

charges  mutual  repidsion  will  take  place  whenever  they  are 
brought  near  each  other.  If  a  stick  of  sealmg-zvax^  elec- 
trified by  being  rubbed  with  fur,  is  approached  to  another 
pendulum,  the  same  results  will  be  produced — the  ball  will 
fly  towards  the  wax,  and  after  contact  will  again  be  re- 
pelled. But  the  charges  respectively  developed  in  these 
two  cases  are  not  in  the  same  condition.  For  if  after  the 
pith-ball  has  been  touched  with  the  glass  rod  and  repelled, 
the  electrified  sealing-wax  be  brought  in  the  vicinity,  attrac- 
tion takes  place  between  the  ball  and  sealing-wax.  Similarly, 
if  the  pendulum  be  charged  with  the  electrified  sealing-wax, 
the  ball  will  be  repelled  by  the  wax  and  attracted  by  the 
glass  rod. 

We  have,  therefore,  to  distinguish  between  two  kinds  of 
electrification — that  produced  by  rubbing  glass  with  silk 
and  that  produced  by  rubbing  sealing-wax  with  fur. 

To  make  this  distinction  clear,  the  following  designations 
have  been  adopted : 

An  electric  charge  excited  upon  glass  by  rubbing  it  with 
silk  has  been  termed  a  positive  charge  (+),  and  that 
developed  on  resinous  bodies  by  friction  with  flannel  or  fur 
a  negative  charge  (  — )• 

2206.  Neither  charge  is  produced  alone,  for  there  is 
always  an  equal  quantity  of  both  charges  produced,  one 
charge  appearing  on  the  body  rubbed,  and  an  equal  amount 
of  the  opposite  charge  upon  the  rubber. 

2207.  The  inte7isity  of  the  charge  developed  by  rubbing 
the  two  substances  together  is  evidently  independent  of  the 
actual  amount  of  friction  which  takes  place  between  the 
bodies.  For,  in  order  to  obtain  the  highest  possible  degree 
of  electrification  from  two  dissimilar  substances,  it  is  only 
necessary  to  bring  every  portion  of  one  surface  into  intimate 
contact  with  every  particle,  or  every  portion  of  the  other 
surface ;  when  this  is  done,  no  extra  amount  of  rubbing  can 
develop  any  greater  charge  upon  either  substance. 

2208.  From  these  experiments  are  derived  the  follow- 
ing laws: 


1452  PRINCIPLES  OF 

When  two  dissimilar  substances  are  placed  in  contact^  one 
of  them  always  assumes  the  positive  afid  the  other  the  nega- 
tive condition^  altJiough  t lie  amount  may  sometimes  be  so  small 
as  to  render  its  detection  very  difficult. 

Electrified  bodies  with  similar  charges  are  mutually  re- 
pellent, while  electrified  bodies  zvith  dissimilar  charges  are 
mutually  attractive. 

2209.  Table  71  gives  a  list  called  the  electric  series, 

where  the  substances  are  arranged  in  such  order  that  each 
receives  a  positive  charge  when  rubbed  with  any  of  the 
bodies  following,  and  a  negative  charge  when  rubbed  with 
any  of  those  which  precede  it: 

TABLE    71. 

THE    ELECTRIC    SERIES. 

1.  Fur.  6.  Cotton.  11.   Sealing-wax. 

2.  Flannel.  7?  Silk.  12.   Resin. 

3.  Ivory.  8.  The  body.  13.   Sulphur. 

4.  Crystals.  9.  Wood.  14.   Gutta-percha. 

5.  Glass.  10.  Metals.  15.   Gun-cotton. 

For  example,  glass  when  rubbed  with  fur  receives  a 
negative  charge;  but  when  rubbed  with  silk,  it  receives  a 
positive  charge. 

ELECTROSTATIC  IIVSTRUMEIVTS. 

221 0.  The  electroscope  is  an  instrument  for  detect- 
ing static  charges  of  electricity  and  for  determining  their 
condition,  whether  positive  or  negative;  but  not  for  meas- 
uring the  intensity  of  the  charges. 

The  pith-ball  suspended  by  a  silk  thread  acts  as  a  simple 
electroscope.  A  more  sensitive  electroscope  is  shown  in  Fig. 
902,  and  consists  of  two  gold  leaves  suspended  within  a  glass 
jary,  which  serves  to  protect  them  from  drafts  of  air  and  to 
support  them  from  contact  with  the  earth.  The  gold  leaves 
a  are  supported  side  by  side  in  the  jar  by  a  brass  rod  or  wire 
b  which  passes  through  a  cork  in  the  mouth  of  the  jar.  The 
upper  end  of  the  brass  rod  is  furnished  with  a  fiat  metallic 


ELECTRICITY  AND  MAGNETISM. 


1453 


Fig.  903. 


plate  or  ball  c.  An  electrified  body,  such  as  the  rod  d, 
brought  into  the  vicinity  of  the  electroscope,  will  cause  the 
leaves  to  repel  one 
another,  due  to  the  fact 
that  they  are  both  sim- 
ilarly electrified. 

To  deternime  the  con- 
ditioii  of  a  charge  by 
the  electroscope :  First, 
charge  the  gold  leaves 
with  a  known  charge, 
such  as  that  developed 
upon  glass  when  rubbed 
with  silk.  The  leaves 
will  spread  apart,  be- 
ing electrified  with  a 
positive  charge.  When 
they  are  thus  charged,  the  approach  of  a  body  which  is 
positively  charged  will  cause  them  to  open  still  more  widely ; 
while  on  the  approach  of  one  negatively  charged,  they  will 
close  together. 

2211.     The  torsion  balance  is  an  instrument  used  to 
measure  Wi^  force  exerted  between  two  electrified  bodies. 

It  consists  of  an  arm  or  lever  of  some  light  insulating 
material,  such  as  a  straw  or  piece  of  wood,  provided  at  one 
end  with  a  gilt  pith-ball  n,  Fig.  903,  and 
suspended  in  a  glass  jar  by  a  fine  silver 
wire.  The  wire  passes  up  through  a 
glass  tube  and  is  fastened  to  a  brass 
stopper  b^  called  the  torsion  bead.  The 
torsion  head  is  graduated  in  degrees,  and 
is  capable  of  being  revolved  around  upon 
the  glass  tube.  Another  gilt  pith-ball 
in  is  fastened  to  the  end  of  the  vertical 
glass  rod  «,  which  is  inserted  through  an 
opening  in  the  top  of  the  jar.  A  narrow 
strip  of  paper,  also  divided  into  degrees, 
encircles  the  glass  jar  at  the  level  of  the  two  pith-balls. 


Fig.  90.3. 


1454  PRINCIPLES  OF 

221)2.  To  use  the  torsion  balance:  Turn  the  torsion 
head  around  until  the  two  pith-balls  m  and  n  just  touch 
each  other.  Remove  the  glass  rod  «,  and  communicate  the 
charge  to  be  measured  to  the  gilt  ball  vi.  Replace  the  glass 
rod  in  the  jar.  The  two  gilt  balls  will  touch  each  other 
momentarily,  and  half  of  the  charge  will  pass  from  in  to  n. 
As  both  balls  possess  similar  charges,  they  will  immediately 
repel  each  other;  the  ball  ;/,  being  driven  around,  twists  up 
the  wire  to  a  certain  extent.  The  force  of  torsion  in  the 
wire  will  eventually  balance  the  force  of  repulsion,  and  the 
ball  n  will  come  to  rest  when  the  balls  are  separated  by  a 
certain  distance.  In  any  wire,  the  force  of  torsion  is  pro- 
portional to  the  amount  of  twist,  or,  in  this  case,  to  the  angle 
of  torsion  ;  hence,  the  force  exerted  between  the  two  balls 
can  be  measured  by  the  angle  described  by  the  ball  n. 

2213.  By  means  of  the  torsion  balance,  it  is  proven 
that  the  force  exerted  betzveen  tzvo  bodies  statically  charged 
with  electricity  varies  inversely  as  the  square  of  the  distance 
betzveen  them. 

Thus,  suppose  two  electrified  bodies  one-fourth  inch 
apart  repel  each  other  with  a  certain  force ;  at  a  distance 
of  one  inch  the  force  would  only  be  one-sixteenth  as  great. 
This  law  is  equally  true  for  the  force  of  attraction  between 
two  bodies  with  dissimilar  charges. 

2214.  In  either  case,  whether  of  attraction  or  repul- 
sion, the  force  at  any  given  distance  is  equ-al  to  the  product 
of  the  two  quantities  of  electricity  on  the  bodies.  But  a 
unit  quantity  of  electricity  is  that  charge  which,  when 
placed  in  air  at  a  distance  of  one  centimeter  from  another 
equal  and  similar  charge,  will  be  repelled  with  a  force  of 
one  dyne.  (For  values  of  the  centimeter  and  dyne,  see 
Arts.  2255  and  2262.) 

Therefore,  if  a  certain  body  were  charged  with  4  unit 
quantities  of  electricity  and  another  with  3  tinit  quantities^ 
then  the  force  exerted  between  them  would  be  13  times 
greater  than  if  each  had  contained  a  charge  of  one  unit. 


ELECTRICITY  AND  MAGNETISM.  1455 

CONDUCTORS  AND  INSULATORS. 

2215.  Only  that  part  of  a  dry  glass  rod  which  has 
been  rubbed  will  be  electrified ;  the  other  parts  will  produce 
neither  attraction  nor  repulsion  when  brought  near  an 
electroscope.  The  same  is  true  of  a  piece  of  sealing-wax 
or  resin.  These  bodies  do  not  readily  conduct  electricity ; 
that  is,  they  oppose  or  resist  the  passage  of  electricity 
through  them.  Therefore,  electricity  can  reside  only  as 
a  charge  upon  that  part  of  their  surfaces  where  it  is 
developed.  Experiments  show  that  when  a  metal  receives 
a  charge  at  any  point,  the  electricity  immediately  passes  or 
flows  through  its  substance  to  all  parts.  Metals,  therefore, 
are  said  to  be  good  conductors  of  electricity.  Bodies  have 
accordingly  been  divided  into  two  classes;  namely,  non-con- 
ductors or  insulators^  those  bodies  which  offer  an  infinitely 
high  resistance  to  the  passage  of  electricity ;  and  conductors, 
or  those  which  offer  a  comparatively  low  resistance  to  its 
passage.  This  distinction  is  not  absolute,  for  all  bodies 
conduct  electricity  to  some  extent,  while  there  is  no  known 
substance  that  does  not  offer  some  resistance  to  its  flow. 

2216.  Electrical  resistance  may  be  defined  as  a 
general  property  of  matter,  varying  with  different  sub- 
stances, by  virtue  of  which  matter  opposes  or  resists  the 
passage  of  electricity. 

2217.  Conductivity  is  the  facility  with  which  a  body 
transmits  electricity,  and  is  the  reciprocal,  or  opposite,  of 
resistance.  For  instance,  copper  is  of  low  resistance  and 
high  conductivity;  wood  is  of  high  resistance  and  low 
conductivity. 

Table  72  gives  a  list  of  conducting  and  non-conducting 
substances. 

2218.  In  dividing  the  different  substances  into  two 
classes,  it  should  be  understood  that  it  is  done  only  as  a 
guide  for  the  student.  Between  these  classes  are  many 
substances  which  might  be  included  in  either,  and  no  hard 
or  fast  line  can  be  drawn.     The  list  is  arranged  in  order  of 


1456 


PRINCIPLES  OP 


the  conductivity  of  the  different  substances,  beginning  with 
silver,  which  is  the  best  conductor  known. 

TABLE  72. 

CONDUCTORS  AND   INSULATORS  IN   ORDKR    OF  THEIR 

VALUE. 


Conductors. 

Insulators  (N 

on-Conductors). 

Silver. 

Dry  Air. 

Glass. 

Copper. 

Shellac. 

Mica. 

Other  Metals. 

Paraffin. 

Ebonite. 

Charcoal. 

Amber. 

India-rubber. 

Plumbago. 

Resin. 

Silk. 

Moist  Earth. 

Sulphur. 

Paper. 

Water. 

Wax. 

Oils. 

A  general  idea  of  these  values  may  be  obtained  from  the 
fact  that  water  has  6,754  million  times  greater  resistance 
than  copper. 

ELECTROSTATIC    INDUCTION. 

2219.  An  electric  charge  will  be  induced  \n  a  conductor 
when  that  conductor  is  brought  into  the  vicinity  of  an 
electrified  body.  This  effect  is  termed  electrostatic  in- 
duction, and  the  range  of  space  in  which  it  can  take  place 
is  an  electrostatic  field. 

2220.  If  the  conductor  A  B,  Fig.  904,  is  supported 
from    contact   with    the    earth    by  insulators,    and    is    then 

brought  into  the  elec- 
trostatic field  of  the 
conductor  C,  but  not 
touching  (T,  which  is 
electrified  with  a  posi- 
tive charge,  then: 
1.  A  charge  will  be 
Fig.  904  produced  on  A  B^  as    is 

shown  by  the  pith-balls  spreading  apart. 


ELECTRICITY  AND  MAGNETISM.  1457 

2.  This  charge  will  be  negative  at  the  end  A  nearest  C 
and  positive  at  the  end  B  farthest  from  C,  as  can  be  shown 
by  an  electroscope. 

3.  The  charges  at  A  and  B  are  equal  to  each  other  ;  for 
if  the  conductor  A  B  he  removed  from  the  vicinity  of  the 
conductor  (7  without  having  touched  C,  the  opposite  charges 
immediately  neutralize  each  other;  that  is,  no  electrification 
will  be  indicated  by  the  pith-balls. 

4.  Again,  as  C  is  brought  nearer  and  nearer  A,  the 
charges  of  opposite  signs  on  the  approaching  surfaces 
attract  each  other  more  and  more  strongly  until  C  is  ap- 
proached very  near,  and  then  a  spark  darts  across  the  inter- 
vening space.  Two  charges  rushing  together  neutralize 
one  another,  leaving  the  induced  positive  charge,  which  was 
formerly  repelled  to  the  end  B  of  the  conductor,  as  a  per- 
manent charge  over  all  the  surface  of  A  B. 

5.  Or,  if  the  conductor  y^  ^  be  touched  by  a  conductor 
connected  to  the  earth  when  it  is  under  the  influence  of  C, 
the  positive  charge  will  neutralize  with  the  earth  and  the 
negative  charge  will  remain  when  A  B  i"?,  removed  from  the 
field  of  C.  The  charge  which  passes  to  the  earth  from  A  B 
is  called  a  free  charge,  while  that  charge  which  is  held  by 
the  inductive  influence  of  (7  is  a  bound  charge.  Both  free 
and  bound  charges  can  be  negative  or  positive,  depending 
upon  the  sign  of  the  charge  on  C. 

2221.  When  two  conducting  bodies,  both  electrified 
with  equal  dissimilar  charges,  are  touched  together  momen- 
tarily, the  two  charges  will  neutralize  each  other,  no  trace 
of  either  remaining  ;  but  if  they  are  unequal,  the  smaller 
charge  will  neutralize  an  equal  amount  from  the  larger  and 
leave  a  charge  which  is  equal  to  the  difference  between  the 
two  original  charges,  the  sign  of  the  remaining  charge  being 
the  same  as  that  of  the  larger  one.  Before  the  bodies  can 
be  separated,  the  remaining  charge  will  divide  equally 
between  the  two  bodies.  For  example,  two  gilt  balls  A  and 
B  are  charged  respectively  with  -j-  30  and  —  4  units  of  elec- 
tricity.     When   the   balls  are    placed    in   contact,   the    —  4 


1458  PRINCIPLES  OF 

charge  on  B  will  neutralize  a  +  4  charge  on  A  and  leave  a 
-(-  16  charge,  which  immediately  divides  equally  between 
the  two  balls ;  that  is,  a  charge  of  +  8  units  remains  on 
each  ball  when  they  are  separated. 

It  is  found  that  the  effect  of  this  electrostatic  induction  is 
greatly  increased  by  placing  some  other  substance,  such  as 
glass  or  paper  instead  of  air,  between  the  two  bodies. 

2'2>2>2»  The  facility  with  Avhich  a  body  allows  electro- 
static induction  to  act  across  it  is  called  its  inductive 
capacity.  The  inductive  capacity  varies  with  different  sub- 
stances, bvit  almost  all  non-conductors  are  better  than  air. 

2:2!23.  Any  substance  which  allows  electrostatic  induc- 
tion to  act  across  it  is  termed  a  dielectric.  All  dielectrics 
are  non-conductors.  Table  73  gives  a  list  of  several  non- 
conductors in  the  order  of  their  inductive  capacity  values, 
from  which  it  will  be  seen  that,  with  two  exceptions,  air  has 
the  lowest  inductive  capacity. 

TABLE   73. 

INSULATORS  IN   ORDER   OF   THEIR  INDUCTIVE  CAPACITY 

VALUES. 

Glass.  Paraffin  (solid). 

Shellac.  Carbonic  Acid. 

Sulphur.  Air. 

Ebonite.  Hydrogen. 

India-rubber.  Vacuum. 
Petroleum. 

2224.  The  electrophorus.  Fig.  905,  is  an  instrument 
devised  for  the  purpose  of  obtaining  an  almost  unlimited 
number  of  static  charges  of  electricity  from  one  single 
charge,  and  is  based  upon  the  principle  of  electrostatic  in- 
duction. 

It  consists  of  two  main  parts  :  a  thin  cake  of  resinous 
material  cast  in  a  round  metal  dish  or  pan  B,  about  one  foot 
in  diameter  ;  and  a  round  disk  A,  of  slightly  smaller  diam- 
eter, made  of  metal  and  provided  with  a  glass  handle.  In 
using   the  electrophorus,   the  resinous    cake    must    first    be 


ELECTRICITY  AND  MAGNETISM. 


1459 


beaten  or  rubbed  with  a  warm  piece  of  woolen  cloth  or  fur. 
The  disk  or  cover  is  then  placed  upon  the  cake,  touched 
momentarily  with  the  finger  to  liberate  the  free  charge,  then 
removed  by  taking  it  up  by  the  handle.  It  is  now  found  to 
be  powerfully  electrified  with  a  positive  charge ;  so  much  so, 


Fig.  905. 


indeed,  as  to  yield  a  considerable  spark  when  the  hand  is 
brought  near  it.  The  cover  may  be  replaced,  touched,  and 
again  removed,  and  will  thus  yield  any  number  of  sparks  ; 
the  original  charge  on  the  resinous  plate  meanwhile  remain- 
ing practically  as  strong  as  ever. 

!2!225.  A  static  charge  of  electricity  is  not  usually  dis- 
tributed uniformly  over  the  surface  of  conducting  bodies. 
Experiments  show  that  there  is  more  electricity  on  the 
edges  and  corners  than  upon  their  flatter  parts. 

The  term  electric  density  is  used  to  signify  the  amount 
or  quantity  of  electricity  residing  on  a  small  area  of  any 
part  of  a  body,  the  distribution  being  supposed  to  be  uni- 
form over  that  small  part  of  the  surface. 

The  electric  density  is  the  quotient  arising  from  dividing 
the  total  charge  of  electricity  in  units  of  quantity  residing 
upon  the  surface  of  a  body,  by  the  area  of  the  surface  in 
square  inches.  For  example,  a  charge  of  240  units  of  elec- 
tricity is  imparted  to  a  sphere,  the  surface  area  of  which  is 
40  square  inches  ;  then,  the  electric  density  over  the  surface 
of  the  sphere  is  ^-f-^-  =  6  units  of  electricity  per  square  inch. 


1460 


PRINCIPLES  OF 


ELECTROSTATIC   MACHINES. 

2226.  Electrostatic  machines  have  been  devised 
for  the  purpose  of  obtaining  larger  static  charges  than  can 
be  developed  by  rubbing  a  glass  rod  or  by  the  electrophorus. 
They  consist,  mainly,  of  two  parts,  one  for  producing  and 
the  other  for  collecting  the  charges. 

There  are  three  important  kinds  of  electrostatic  machines — 
the  cylinder^  ihQ  plate,  and  the  induction  machines. 

2227.  The  cylinder  machine,  as  usually  constructed, 
consists  of  three  principal  parts:  (1)  a  cylinder  of  glass 
revolving  upon  a  horizontal  axis;  (2)  a  rubber  or  cushion  of 
horsehair,  to  which  is  attached  a  long  silk  flap,  and  (3)  an 
insulated  metallic  cylinder  called  a  prime  conductor.  In 
Fig.  90G  the  cushion  of  horsehair  a,  covered  with  a  coating 
of  amalgam  of  zinc,  presses  against  the  glass  cylinder  b  from 


Fig.  906. 


behind,  allowing  the  silk  flap  s  to  rest  upon  the  upper  half 
of  the  glass.  The  prime  conductor  C  is  provided  at  one 
end  with  a  row  of  fine  metallic  spikes,  and  is  placed  in  front 
of  the  machine  with  the  row  of  spikes  projecting  towards  the 
glass  cylinder.  When  the  glass  cylinder  is  revolved,  a 
positive  charge  is  produced  vipon  the  glass  and  a  negative 
charge  upon  the  rubber.  The  positive  charge  is  carried 
around  upon  the  glass  cylinder,  and  just  before  reaching  a 
position  opposite  the  row  of  spikes  it  acts  inductively  upon 
the  prime  conductor,  attracting  a  negative  charge  to  the 
near  end  and  repelling  a  positive  charge  to  the  far  end. 
When  the  positive  charge  arrives  in  front  of  the  row  of 


ELECTRICITY  AND  MAGNETISM.  1461 

spikes,  it  will  be  neutralized  by  the  attracting  negative  charge 
from  the  conductor,  leaving  the  glass  in  a  neutral  condition 
ready  to  be  excited  again.  A  positive  charge  now  remains 
upon  the  prime  conductor,  and  can  be  utilized  for  other 
experiments. 

2228.  The  plate  macliiiie  is  similar  in  all  respects  to 
the  cylinder  machine,  with  the  exception  that  a  glass  or 
ebonite  plate  is  used  instead  of  the  glass  cylinder,  and  there 
are  usually  two  sets  of  rubbers  or  cushions  instead  of  one. 
Each  set  of  cushions  is  double ;  that  is,  it  is  made  in  two 
parts,  with  the  plate  revolving  between  them.  One  set  of 
cushions  is  placed  at  the  top  of  the  machine,  and  the  other 
at  the  bottom,  with  silk  flaps  extending  from  each  over  a 
quadrant  of  the  plate.  The  charge  is  collected  on  two 
prime  conductors  connected  by  a  metal  rod,  and  each  is  pro- 
vided with  a  row  of  fine  spikes  at  one  end.  They  are  placed 
in  such  a  position  that  the  two  rows  of  fine  spikes  project 
towards  the  glass  plate  at  opposite  sides  of  its  horizontal 
diameter.  The  electrostatic  action  of  the  machine  is  in  all 
respects  the  same  as  that  of  the  cylinder  machine. 

2229.  The  induction  machine  differs  widely  in  its 
action  from  the  two  machines  previously  described.  It 
requires  an  initial  charge  from  some  exterior  source  to  start 
its  action.  The  initial  charge  acts  inductively  across  a 
revolving  glass  plate  and  produces  other  charges;  these 
charges  in  turn  are  conveyed  by  the  moving  parts  to  some 
other  point,  where  they  increase  the  initial  charge,  or  fur- 
nish a  supply  of  electricity  to  a  prime  conductor. 

The  two  principal  machines  of  this  class  are  the  Holtz 
and  the  "Wimshurst. 

THE    CONDEIVSER, 

2230.  It  has  been  shown  that  opposite  charges  attract 
and  hold  one  another;  that  electricity  can  not  flow  through 
glass,  and  yet  can  act  across  it  by  induction.  If  a  piece  of 
tin-foil  is  stuck  upon  the  middle  of  each  face  of  a  thin  plate 
of  glass,  and  one  of  the  pieces  is  electrified  with  a  positive 


1463  PRINCIPLES  OF 

charge  and  the  other  with  a  negative  charge,  the  two  charges 
will  attract  one  another,  or,  in  other  words,  they  are  held 
or  bound  by  each  other.  It  will  be  found  that  these  two 
pieces  of  tin-foil  may  be  charged  a  great  deal  stronger  in 
this  manner  than  either  of  them  could  possibly  be  if  they 
were  stuck  to  the  glass  alone  and  then  electrified.  This 
property  of  retaining  and  accumulating  a  large  quantity  of 
static  charges  which  two  conductors  possess  when  placed 
side  by  side  and  separated  from  each  other  by  a  non-con- 
ductor, is  called  their  capacity. 

)2231.  A  condenser  is  an  apparatus  for  condensing  or 
accumulating  a  large  quantity  of  static  charges  of  electricity 
on  a  comparatively  small  surface,  and  consists  of  two  con- 
ductors separated  by  a  thin  layer  of  some  non-conducting 
material.  One  of  the  plates  is  entirely  insulated  from  the 
earth,  and  the  other  is  connected  to  it  by  a  conductor. 

The  capacity  of  a  condenser  depends  upon  (1)  the  size 
and  form  of  the  condensing  plates,  (2)  the  thinness  of  the 
insulating  material  between  them,  and  (3)  the  inductive 
capacity  of  the  insulating  material. 

2232.  A  convenient  form  of  condenser  is  called  the 
Leyden  jar,  Fig.  907.      It  consists  of  a  glass  jar  J  coated 

C 


Fig.  907. 


up  to  a  certain  height  on  the  inside  and  outside  with  tin> 
foil.  A  brass  knob  a  is  fixed  on  the  end  of  a  stout  brass 
wire,  which  passes  downwards  through  a  lid  or  stopper  of 
dry,  well-varnished  wood,  and  connected  by  a  loose  bit 
of  brass  chain  with  the  inner  coating  of  the  jar. 


ELECTRICITY  AND  MAGNETISM.  1463 

To  charge  the  jar,  the  knob  is  held  to  the  prime  con- 
ductor C  of  an  electrical  machine,  the  jar  being  either  held 
in  the  hand  by  the  outer  tin-foil  coating  or  connected  to  the 
earth  by  a  wire  or  chain.  When  a  positive  charge  is  thus 
imparted  to  the  inner  coating,  it  acts  inductively  on  the 
outer  coating,  attracting  a  negative  charge  in  the  face  of 
the  outer  coating  nearest  the  glass,  and  repelling  a  positive 
charge  to  the  outside  of  the  outer  coating.  This  outer 
charge  then  passes  through  the  hand  or  any  conductor  to 
the  earth. 

2233.  An  electrostatic  battery  consists  of  a  num- 
ber of  Leyden  jars  whose  inside  coatings  are  all  connected 
together  and  "whose  outside  coatings  are  all  connected  to 
the  earth. 

ELECTRODYNAMICS. 


POTENTIAL    AND    CURRENT. 

2234.  In  dealing  with  electric  currents,  the  v^oxA  poten- 
tial will  be  substituted  for  the  general  and  vague  phrase 
electrical  condition. 

The  term  potential,  as  used  in  electrical  science,  is  anal- 
ogous yNxX^x  pressure  in  gases,  head  in  liquids,  and  tempera- 
ture in  heat. 

When  an  electrified  body,  positively  charged,  is  connected 
to  the  earth  by  a  conductor,  electricity  is  said  to  jioiv  from 
the  body  /c  the  earth;  and,  conversely,  when  an  electrified 
body  negatively  charged  is  connected  to  the  earth,  electricity 
is  said  to  Jlow  from  the  earth  to  that  body.  That  which 
determines  the  direction  of  flozu  is  the  relative  electrical 
potential  or  presszcre  of  the  two  charges  in  regard  to 
the  earth. 

2235.  It  is  impossible  to  say  with  certainty  in  which 
direction  electricity  really  flows,  or,  in  other  words,  to 
declare  which  of  two  points  has  the  higher  and  which  the 
lower  electrical  potential  or  pressure.  All  that  can  be  said 
with  certainty  is,  that  when  there  is  a  difference  of  electrical 


1464  PRINCIPLES  OF 

potential,  or  pressure^  an  electric  current  tends  to  ^ow  from 
the  point  of  higher  to  that  of  lower  potential  or  pressure. 

For  convenience,  it  has  been  arbitrarily  assumed  and 
universally  adopted  that  that  electrical  condition  called 
positive  \^  2X  z.  higJier  potential  or  pressure  than  that  called 
negative,  and  that  an  electric  current  flows  from  a  posi- 
tively to  a  negatively  electrified  body. 

2236.  The  zero  or  normal  level  of  water  is  taken  as 
that  of  the  surface  of  the  sea,  and  the  normal  pressure  of 
air  as  that  of  the  atmosphere  at  the  sea-level ;  similarly, 
there  is  a  zero  pressure  or  potential  of  electricity  in  the 
earth  itself.  It  may  be  regarded  as  a  reservoir  of  electricity 
of  infinite  quantity,  and  its  pressure  or  potential  taken  as 
zero.  For  this  reason  all  electric  currents  have  the  ten- 
dency to  reach  this  zero  level,  exactly  as  the  water  on  the 
mountain  top  tends  to  flow  down  to  the  sea-level.  For  this 
reason  it  becomes  necessary  to  insulate  most  electrical 
apparatus,  otherwise  the  electric  current  it  generates  or 
carries  will  leak  away  to  the  earth.  In  Art.  2234  the 
condition  which  is  called  positive  is  assumed  to  be  at  a 
higher  potential  than  the  earth,  and  that  called  negative  is 
assumed  to  be  at  a  lower  potential  than  the  earth. 

It  must  be  understood  that  electricity  is  a  condition  of 
matter  and  not  matter  itself,  for  it  possesses "  neither  weight 
nor  extension.  Consequently,  the  statement  that  electricity 
is  flowing  through  a  conductor  must  not  be  taken  too  liter- 
ally; it  must  not  be  supposed  that  any  material  substance, 
such  as  a  liquid,  is  actually  passing  through  the  conductor 
in  the  same  sense  as  water  flows  through  a  pipe.  The 
statement  that  electricity  is  flowing  through  a  conductor  is 
only  another  way  of  expressing  the  fact  that  the  conductor 
and  the  space  surrounding  it  are  in  different  conditions  than 
usual,  and  that  they  possess  unusual  properties.  The  action 
of  electricity,  however,  is  quite  similar  in  many  respects  to 
the  flow  of  liquids,  and  the  study  of  electric  currents  is 
much  simplified  by  the  analogy. 


ELECTRICITY  AND  MAGNETISM.  1465 

ZSST.  In  order  to  produce  what  is  called  an  electric 
current^  it  is  first  necessary  to  caitse  a  difference  of  electrical 
potential  or  pressure  between  two  bodies  or  between  two  parts 
of  the  same  body. 

In  Art.  2208  it  was  stated  that  when  two  dissimilar 
substances  are  simply  placed  in  contact,  one  always  assumes 
the  positive  and  the  other  the  negative  condition ;  in  other 
words,  a  difference  of  electrical  potential  is  developed  be- 
tween the  two  bodies. 

Placing  a  piece  of  copper  and  zinc  in  contact  will  develop 
a  difference  of  electrical  potential  which  can  easily  be 
detected.  The  same  results  will  follow  if  the  plates  are 
slightly  separated  from  each  other  and  placed  in  a  vessel 
containing  saline  or  acidulated  water,  leaving  a  small  por- 
tion of  one  end  of  each  plate  exposed.  The  exposed  ends 
of  the  zinc  and  copper  are  now  electrified  to  different 
degrees,  or,  in  other  words,  there  is  a  difference  of  electrical 
potential  between  the  plates,  one  plate  being  at  a  higher 
potential  than  the  other. 

When  the  exposed  ends  are  connected  together  by  any 
conducting  material,  the  potential  between  the  plates  tends 
to  equalize,  and  a  momentary  rush  or  discharge  of  elec- 
tricity passes  between  the  exposed  ends  through  the  con- 
ducting material  and  between  the  submerged  ends  through 
the  liquid.  During  its  passage  through  the  liquid,  the 
electricity  causes  certain  chemical  changes  to  take  place; 
these  chemical  reactions  cause  in  their  turn  a  fresh  differ- 
ence of  potential  between  the  plates,  which  is  followed  im- 
mediately by  another  equalizing  discharge,  and  that  by  a 
further  difference,  and  so  on.  These  changes  follow  one 
another  with  great  rapidity — so  rapidly,  in  fact,  that  it  is  im- 
possible to  distinguish  them  apart,  and  they  appear  abso- 
lutely cojitinuous.  The  equalizing  flow  which  is  constantly 
taking  place  from  one  plate  to  the  other  is  knoAvn  as  a  con- 
iiiiuous  current  of  electricity.  Consequently,  an  electric 
current  becomes  cqntimious  zvhen  the  difference  of  potential  is 
constantly  maintained. 

By  the  use  of  a  very  delicate  electroscope,  the  exposed 


1466  PRINCIPLES  OF 

end  of  the  copper  will  be  found  to  be  electrified  with  ^posi- 
tive charge  and  the  submerged  end  with  a  negative  charge ; 
in  the  case  of  the  zinc,  the  opposite  conditions  exist,  namely, 
the  exposed  end  is  electrified  with  a  negative  charge  and  the 
submerged  end  with  a  positive  charge.  The  current,  there- 
fore, will  flow  from  the  exposed  end  of  the  copper  through 
the  conductor  to  the  exposed  end  of  the  zinc,  and  from  the 
submerged  end  of  the  zinc  through  the  liquid  to  the  sub- 
merged end  of  the  copper. 


VOL-XAIC   ELECTRICITY. 

3238.     The  two  Italian  physicists,  Volta  and  Galvani, 
/O'''*'*'^^  first    constructed    the    so-called 

//  J  simple    voltaic    or    galvanic 

C|Af      ^KM"  cell,  as  shown  in  Fig.  908.      It  is 

^^  |l^-T||rt  an    apparatus    for    developing  a 

H    ir^^i  ill  id  continuous  current  of  electricity, 

Ip^jJjJI^ysJ^^  and    consists,    essentially,    of    a 

||]||||]^^  vessel   A,    containing    saline    or 

IiIjIII  '  ,„  J||B    fe     acidulated  water,  into  which  are 
ii^''*liH|l~^-^i^  submerged  two  plates  of  dissimi- 

J  ill!]  liill  liliiiiiiilliilliiilljlal^E  lar    metals,    C    and    Z,    or    one 
"^^^^3|lill|iil^^P^^     metal  and  a  metalloid. 

Fig.  908.  Electrolyte  is  the  name  given 

to  the  liquid  which,  as  it  transmits  the  current,  is  decom- 
posed by  it. 

The  two  dissimilar  metals,  when  spoken  of  separately,  are 
called  voltaic  elements  ;  when  taken  collectively,  they 
are  known  as  a  voltaic  couple. 

2239.  A  voltaic  battery  is  a  number  of  simple  voltaic 
cells  properly  joined  together. 

Electrodes  or  poles  of  a  cell  or  battery  are  metallic 
terminals  attached  to  the  plates,  and  are  used  to  connect 
the  cell  or  battery  to  any  exterior  conductor  or  to  another 
cell  or  battery. 

It  should  be  remembered  that  the  polarity  of  that  end  of 
the  plate  or  voltaic  element  which  is  acted  upon  by  the  elec- 


ELECTRICITY  AND  MAGNETISM.  1467 

trolyte  is  always  of  opposite  sign  to  its  electrode.  For 
instance,  in  the  case  of  the  zinc  and  copper,  the  electrode 
fastened  to  the  zinc  would  be  spoken  of  as  the  negative  elec- 
trode of  the  cell,  while  the  zinc  itself  would  be  the  positive 
element  of  the  cell,  its  submerged  end  being  positive. 


CHEMICAL    ACTIOIV    IIV    A    SIMPLE    CELL. 

2240.  When  a  piece  of  ordinary  zinc  is  placed  alone  in 
sulphuric  acid  diluted  with  water,  the  zinc  is  attacked  by  the 
acid,  and  a  part  of  it  is  dissolved  into  a  salt  of  that  metal, 
called  sulpJiate  of  zinc.  At  the  same  time  the  liquid  is  de- 
composed and  hydrogen  gas  is  liberated  from  it,  coming  up 
from  around  the  zinc  in  small  bubbles,  and  the  whole  mass 
of  the  liquid  becomes  heated.  If  the  zinc  is  absolutely  pure, 
the  chemical  actions  take  place  more  slowly;  the  bubbles  of 
liydrogen  do  not  immediately  rise  to  the  surface,  but  form 
around  the  zinc,  protecting  it  from  further  action  of  the 
acid.  By  placing  another  metal  in  the  water,  say  a  piece  of 
copper,  and  connecting  its  exposed  end  with  that  of  the 
zinc  by  a  conductor,  the  chemical  actions  become  exceed- 
ingly vigorous  again.  Large  quantities  of  Jiydrogen  gas  are 
again  liberated,  but  instead  of  the  bubbles  appearing  around 
the  zinc,  they  form  around  the  copper  and  come  to  the  sur- 
face at  that  place;  the  energy  which  in  the  former  case  was 
expended  in  heating  the  liquid  now  appears  in  the  form  of 
electric  energy.  Whenever  the  connection  betAveen  the  ex- 
posed ends  is  broken,  all  chemical  actions  cease  and  remain 
inactive  until  the  two  metals  are  again  connected. 

2241.  In  any  voltaic  cell  the  element  which  is  acted 
upon  by  the  electrolyte  will  always  be  the  positive  element, 
and  its  electrode  the  negative  electrode  of  the  cell. 

The  differences  of  electric  potential,  however,  between 
the  different  pairs  of  metals  are  not  all  equal.  In  Table  74 
various  materials  are  arranged  in  a  series,  such  that  each 
substance  enumerated  becomes  positively  electrified  when 
placed  in  contact  with  any  one  below  it  in  the  series. 


1468  PRINCIPLES  OP 

TABLE    74. 
THE   ELECTROMOTIVE    SERIES. 

1.  +  Sodium.  5.   Tin.  9.  Gold. 

2.  Magnesium.  6.   Iron.  10.  Platinum. 

3.  Zinc.  7.  Copper.  11.  ~  Graphite  (carbon). 

4.  Lead.  8.   Silver. 

2242.  The  term  electromotive  force,  2iS2ially  zuritten 
E.  M.  F.,  is  employed  to  denote  that  ivhicJi  moves  or  tends  to 
move  electricity  from  one  place  to  another. 

In  the  case  of  two  substances  placed  in  contact,  either 
directly  or  by  a  liquid,  the  resulting  electromotive  force  is 
due  to  the  difference  of  potential.  Just  as  in  water-pipes  a 
difference  of  level  produces  a  pressure^  and  the  pressure  pro- 
duces 2i  ffozv,  as  soon  as  the  water  is  turned  on,  so  differ e7ice 
of  potential  produces  electromotive  force^  and  electromotive 
force  sets  up  a  current^  as  soon  as  the  circuit  is  completed 
through  which  the  electricity  may  flow. 

2243.  Any  two  of  the  substances  of  T^le  74  form  a 
voltaic  couple,  and  produce  a  difference  of  potential  when 
submerged  in  saline  or  acidulated  water;  the  one  standing 
first  on  the  list  being  the  positive  element  or  plate  and  the 
other  the  negative.  For  example,  if  iron  and  graphite  are 
used,  the  iron  will  be  acted  upon  by  the  liquid,  and  will  form 
th& positive  element;  but  if  iroii  and  ^-/wi^'are  used,  the  sine 
will  be  acted  upon  by  the  liquid,  and  will  form  the  positive 
element. 

The  difference  of  potential  will  be  greater  in  proportion 
to  distance  between  the  positions  of  the  two  substances  in 
the  list.  For  example,  the  difference  of  potential  developed 
between  zinc  and  graphite  is  much  greater  than  that  devel- 
oped between  zijic  and  iron  ;  in  fact,  the  difference  of  poten- 
tial developed  between  zi7ic  and  graphite  is  equal  to  the 
difference  of  potential  developed  between  zinc  and  iron  plus 
that  developed  between  iron  and  graphite. 

2244.  Electricity  flowing  as  a  current  differs  from 
static    charges    in    three    important    degrees,     namely,    its 


ELECTRICITY  AND  MAGNETISM. 


14G9 


potential  is  much  lower,  its  actual  quantity  is  larger,  and  it 
is  continuous. 

A  strong  voltaic  battery  of  several  cells  produces  only  a 
slight  effect  upon  a  gold-leaf  electroscope,  and,  apparently, 
none  of  its  parts  possesses  the  property  of  attracting  light 
substances.  'Y:h.Q  potential  oi  a  current  of  electricity  is  com- 
paratively so  small  that  a  voltaic  battery  composed  of  a 
large  number  of  cells  is  not  sufficient  to  produce  a  spark  of 
more  than  one  or  two  hundredths  of  an  inch  in  air,  whereas 
a  small  electrostatic  machine  will  produce  sparks  several 
inches  in  length.  If,  however,  the  actual  quantity  of  elec- 
tricity is  measured  by  its  eft"ects  in  decomposing  water,  then 
the  quantity  produced  by  a  simple  voltaic  cell  as  small  as  a 
thimble  would  give  greater  results  than  that  from  an  elec- 
trostatic machine  with  plates  two  or  three  feet  in  diameter. 

An  electric  current  can  not  be  developed  upon  the  surfaces 
of  non-condiLcting  substances  by  current  electricity,  as  in 
the  case  of  static  charges,  and  it  will  never  flow  unless  the 
conducting  path  is  made  entirely  of 
conducting  material. 


2245.  A  number  of  contacts  of 
dissimilar  metals  can  be  so  arranged  as 
to  add  their  electrical  effects  together; 
the  difference  of  potential  then  devel- 
oped will  be  greater  in  proportion  to 
the  number  of  contacts.  Such  an  ar- 
rangement is  called  a  voltaic  pile. 
(See  Fig.  909. )  It  is  made  by  placing  a 
pair  of  disks  of  zinc  (chemical  symbol, 
Zyi)  and  copper  (chemical  symbol,  Cic) 
in  contact  with  one  another,  and  then 
laying  a  piece  of  flannel  or  blotting- 
paper,  moistened  with  brine,  upon  the 
copper  disk.  The  pair  of  disks  now 
form  a  voltaic  couple.  Several  voltaic 
couples  are  placed  together,  and  each 
pair  separated  by  a  moistened  piece  of 


Fig.  909- 


1470  PRINCIPLES  OF 

flannel  or  blotting-paper.  One  end  of  such  a  pile  would 
then  be  terminated  by  a  disk  of  copper  and  the  other  by  a 
disk  of  zinc.  The  copper  forms  the  positive  electrode  and 
the  zinc  the  negative  electrode.  By  joining  these  two 
electrodes  together  with  a  conductor,  a  current  will  flow 
from  the  positive  to  the  negative  tJirough  the  conductor, 
and  from  the  negative  to  the  positive  through  the  contacts. 


THERMOELECTRIC  CURRENTS. 

2246.  The  difference  of  potential  developed  by  the 
mere  contact  of  two  dissimilar  metals  varies,  not  only  with 
the  kind  of  metals  and  the  physical  condition  of  each,  but 
also  with  their  temperatiLre. 

The  greater  difference  of  potential  developed  by  heat  can 
be  shown  by  soldering  one  end  of  a  bar  of  copper  to  one  end 
of  a  bar  of  zinc,  and  applying  heat  to  the  juncture  so  as  to 
raise  its  temperature  above  that  of  the  other  parts  of  the 
bars.  By  joining  the  free  ends  together  with  a  conductor, 
a  current  of  electricity  will  be  found  to  flow  from  the  zinc 
through  the  contact  to  the  copper;  then  from  the  free  end 
of  the  copper  to  the  free  end  of  the  zinc  through  the  con- 
ductor. If  the  junction  be  cooled  below  the  other  parts  of 
the  bars,  a  current  is  produced  in  the  opposite  direction, 
that  is,  from  the  copper  through  the  contact  to  the  zinc, 
etc.  Even  the  same  metal  in  different  physical  conditions 
will  develop  a  difference  of  potential  if  heated  in  a  certain 
place.  For  instance,  take  a  copper  wire,  part  of  which  is 
straight  and  the  remainder  bent  into  a  spiral,  and  heat  the 
place  where  the  spiral  begins.  Under  these  conditions,  a 
difference  of  electrical  potential  will  be  developed  between 
the  two  free  ends. 

In  general,  the  difference  of  potential  is  larger  in.  propor- 
tion as  the  difference  of  temperature  increases.  With  ex- 
treme temperatures,  however,  this  condition  changes,  and 
at  a  certain  temperature  of  the  junction  no  difference  of 
potential  whatever  is  noticed.  This  temperature  is  called 
the  neutral  temperature.     When  the  junction  is  heated 


ELECTRICITY  AND  MAGNETISM.  1471 

beyond  the  neutral  temperature,  inversion  takes  place,  that 
is,  the  direction  of  the  current  changes. 

2247.  Electric  currents  produced  by  a  change  of 
temperature  are  called  thermoelectric  currents. 

On  account  of  the  small  difference  of  potential  of  thermo- 
electric currents,  they  have  not  been  found  of  great  practical 
value ;  in  fact,  they  often  become  a  source  of  great  annoy- 
ance and  error  in  accurate  measurements  with  delicate 
instruments. 

CIRCUITS. 

2248.  A  circuit  is  a  path  composed  of  a  conductor, 
or  of  several  conductors  joined  together,  through  which  an 
electric  current  flows  from  a  given  point  around  the  con- 
ducting path  back  again  to  its  starting-point 

A  circuit  is  broken  or  opened  when  its  conducting 
elements  are  disconnected  in  such  manner  as  to  prevent  thes; 
current  from  flowing. 

A  circuit  is  closed  or  completed  when  its  conducting 
elements  are  so  connected  as  to  allow  the  current  to  pass. 

A  circuit  in  which  the  conductors  have  come  into  contact 
with  the  ground,  or  with  some  electric  conductor  leading  to 
the  ground,  is  said  to  be  a  grounded  circuit,  or  is  called 
an  earth. 

The  external  circuit  is  that  part  of  a  circuit  which  is 
outside  or  external  to  the  electric  source. 

The  internal  circuit  is  that  part  of  a  circuit  which  is 
included  within  the  electric  source. 

In  the  case  of  the  simple  cell,  the  internal  circuit  consists 
of  the  two  metallic  plates,  or  elements,  and  the  liquid,  or 
electrolyte;  an  external  circuit  would  be  a  wire  or  any  con- 
ductor connecting  the  free  ends  of  the  electrodes  together. 

2249.  A  circuit  divided  into  two  or  more  branches, 
each  branch  transmitting  part  of  the  current,  is  a  divided 
circuit ;  the  conductors  forming  these  branches  are  said  to 
be  connected  in  parallel  or  multiple  arc.  Each  branch 
taken  separately  is  called  a  shunt. 


1473  PRINCIPLES  OF 

Conductors  are  said  to  be  connected  in  series  when  they 
are  so  joined  as  to  allow  the  current  to  pass  through  each 
successively. 


%MX\%\ 


2250.     A  battery  of  voltaic  cells  is  said  to  be  connected 

in  multiple  arc  or  par- 
allel   when    the    positive 
electrodes  of  all  the  cells 
^'°-  ^^^-  are  connected  to  one  main 

positive  conductor  and  all  the  negative  electrodes  are  con- 
nected to  one  main  negative  conductor,  as  shown  in  Fig.  910. 
A  battery  of  voltaic  cells  is  said  to  be  connected  in  series 
when    the    cells    are     ar-       .  i 

ranged  in  one   circuit  by       Vj^^^^^^,i^,i^ji> 
jommg  the  positive    elec-  "'       ~i       "'       "'       "'       "' 

trode    of   one   cell    to    the  ^^°-  ^^^• 

negative  electrode  of  the  adjacent  one,  so  that  the  entire  cur- 
rent passes  successively  through  each,  as  shown  in  Fig.  911. 
When  the  series  and  multiple  connections  are  combined, 

the  battery  is  said  to  be 
connected  in  multiple- 
series  or  parallel- 
it  ijlf  i^^t  ilff  series.  This  is  accom- 
plished by  joining  several 
groups  in  multiple  or 
parallel,  the  cells  in  each  group  being  connected  in  series, 
as  shown  in  Fig.  912. 

ELECTRICAL  UNITS. 

2i2'Sl.  To  properly  measure  the  various  factors  of  an 
electric  circuit,  certain  definite  standards  or  units  must  be 
adopted,  to  which  these  factors  can  be  compared. 

In  every  electrical  circuit  there  are  particularly  three 
factors,  the  true  relation  of  which  must  be  clearly  under- 
stood before  they  can  be  measured. 

These  three  factors  are: 

1.  The  force  tending  to  move  the  electricity. 

2.  The  rate  of  flow  of  the  electricity. 


r 


Fig.  912. 


ELECTRICITY  AND  MAGNETISM.  1473 

3.  The  resistance  which  the  force  must  overcome  to  pro- 
duce the  flow  of  electricity. 

These  factors  are  respectively  termed : 

1.  The  electromotive  force  (written  E.  M.  F.  or  E.). 

2.  The  current  (written  C). 

3.  The  resistance  (written  R.). 

2'2>S2'.  The  relation  of  the  three  principal  factors  will  be 
better  understood  by  comparison  with  the  flow  of  water 
through  a  pipe.  The  force  which  causes  the  water  to  flow 
through  the  pipe  is  due  to  the  Jiead  ox  pressure ;  that  which 
resists  the  flow  is  the  friction  of  the  water  against  the  inside 
of  the  pipe,  and  varies  with  circumstances.  The  rate  of 
flow,  or  the  current,  may  be  expressed  m.  gallons  per  minute, 
and  is  a  ratio  between  the  liead  or  pressure  and  the  resistance 
caused  by  the  friction  of  the  water  against  the  inside  of  the 
pipe.  For,  as  the  pressure  or  head  increases,  the  rate  of 
flow  or  current  increases  in  proportion;  as  the  resistance 
increases,  the  flow  or  current  diminishes. 

In  the  case  of  electricity  flowing  through  a  conductor,  the 
electromotive  force  corresponds  to  the  pressure  or  head  of 
water,  and  the  resistance  which  a  conductor  offers  to  the 
current  to  the  friction  of  the  water  in  the  pipe.  The 
strength  of  an  electric  current  or  the  rate  of  flow  of  electric- 
ity is  also  a  ratio — a  ratio  between  the  electromotive  force 
and  the  resistance  of  the  conductor  through  which  the  cur- 
rent is  flowing.  This  ratio,  as  applied  to  electricity,  was 
first  discovered  by  Dr.  G.  S.  Ohm,  and  has  since  been  called 
Otun's  la'W. 

2253.  Ohm's  La-w. —  The  strength  of  an  electric  current 
in  any  circuit  is  directly  proportional  to  the  electromotive 
force  developed  in  that  circuit  and  inversely  proportional  to 
the  resistance  of  tJie  circuit ;  i.  e.,  is  equal  to  the  quotient 
arising  from  dividing  the  electromotive  force  by  the  resist- 
ance. 

Ohm's  law  is  usually  expressed  algebraically,  thus  : 


1474  PRINCIPLES  OF 

electromotive  force 


Strength  of  current 


resistance 

and  may  be  written,  by  utilizing  the  symbols  given  in  Art 
2251, 

^~  K 

When  the  values  of  any  two  such  quantities  are  known, 
the  third  can  be  readily  found  ;  for,  by  transposing, 

Before  giving  examples  of  the  application  of  Ohm's  law, 
the  value  and  significance  of  the  various  units  will  be  treated 
upon.  There  are  two  principal  systems  of  units  employed 
in  electrical  science.  They  are,  respectively,  the  funda- 
mental units  and  the  practical  units. 


FUNDAMENTAL,  UNITS. 

2254.  The  fundamental  electrical  units  from  which  the 
practical  units  are  derived,  as  shown  later,  are  based  on  the 
three  factors  mass,  length,  and  time.  They  are,  therefore, 
absolutely  independent  of  all  other  considerations,  and  the 
system  which  they  form  is  hence  termed  the  system  of 
absolute  units. 

These  fundamental  units  are,  respectively, 

1.  The  centimeter  as  the  unit  of  lengtli. 

2.  The  gram  as  the  unit  of  mass. 

3.  The  second  as  the  unit  of  time. 

This  system  is  hence  often  termed  the  centimeter- 
gram-second  system,  and  is  written  C.  G.  S.  system. 

2255.  The  centimeter  represents  ^^qqq^qqq^qqq  of  the 

distance  from  the  pole  to  the  equator  on  the  surface  of 
the  earth,  and  is  equal  to  .3937  inch.  Hence,  1  inch 
equals  2, 54  centimeters,  nearly. 

2256.  The  unit  of  mass  or  quantity  of  matter  is 
the  gram,  and  represents  the  quantity  of  matter  contained 


ELECTRICITY  AND  MAGNETISM.  1475 

in  a  cubic  centimeter  of  pure  water  at  the  temperature  of  its 
maximum  density,  which  is  4°C,,  or  39.3°  F.,  and  is  equal 
in  weight  to  15.432  grains. 

2>2'57.     The  unit  of  time  is  the  second,  and  represents 
part  of  a  mean  solar  day. 


86,400 

The  secondary  units  derived  from  these  fundamental 
units  are  defined  as  follows  : 

2258.  The  unit  of  area  is  the  square  centimeter, 

and  is  the  area  contained  in  a  square,  each  of  whose  sides  is 

one  centimeter  in  length. 

1  square  centimeter  equals  .155  square  inch, 
1  square  inch  equals  6.45  square  centimeters. 

2259.  The  unit  of  volume  is  the  cubic  centimeter, 

and  is  the  volume  contained  in  a  cube,  each  of  whose  edges 
is  one  centimeter  in  length. 

1  cubic  centimeter  equals  .06103  cubic  inch. 

1  cubic  inch  equals  16.387  cubic  centimeters, 

2260.  The  unit  of  velocity,  or  the  rate  at  which  a 
body  moves  from  one  position  to  another,  is  defined  as  the 
velocity  of  a  body  moving  through  unit  distance  (one  centi- 
meter) in  unit  time  (one  second).  The  unit  of  velocity  is, 
therefore,  one  centimeter  per  second. 

Note. — The  word  ^er  in  such  expressions  denotes  that  the  quantity 
named  before  it  is  to  be  divided  by  the  quantity  named  after  it.  Thus, 
to  compute  the  velocity  in  centimeters  per  second,  divide  the  number 
of  centimeters  by  the  number  of  seconds. 

2261.  The  unit  of  acceleration  is  that  accelera- 
tion which  imparts  unit  velocity  to  a  body  in  unit  time,  or 
an    acceleration     of    one    centimeter-per-second    per 

second.  The  acceleration  due  to  gravity  imparts  in  one 
second  a  velocity  considerably  greater  than  this,  for  the 
velocity  it  imparts  to  falling  bodies  is  about  981  centimeters 
per  second  (or  about  33.3  feet  per  second).  The  value 
differs  slightly  in  different  latitudes.     At  New  York  City 


1476  PRINCIPLES  OF 

the  acceleration  of  gravity  is  ^=  980.26  ;  at  the  Equator, 
g^  978.1  ;  at  the  North  Pole,  ^=  983.1. 

)2262.  The  unit  of  force  is  the  dyne,  and  is  that  force 
which,  acting  on  a  mass  of  one  gram  for  one  second,  gives  to 
it  a  velocity  of  one  centimeter  per  second.  For  an  example 
of  force  and  the  application  of  the  unit  of  force,  see  Art. 
2214. 

2263.  The  unit  of  ^work  is  the  erg,  and  is  that 
amount  of  work  performed  when  a  force  of  one  dyne  is 
overcome  through  a  distance  of  one  centimeter  ;  that  is, 
the  work  done  in  pushing  a  body  through  a  distance  of  one 
centimeter  against  a  force  of  one  dyne  ;  the  unit  of  work, 
the  erg,  therefore  equals  one  dyne  centimeter. 

2264.  The  unit  of  energy  is  also  the  erg ;  for  the 

energy  of  a  body  is  measured  by  the  work  it  can  do.  The 
unit  of  energy,  the  erg,  is  therefore  also  one  dyne  centi- 
meter. 

2265.  The  unit  of  power  has  no  particular  name  in 
the  C.  G,  S,  system.  It  is  defined  as  the  rate  of  doing 
work,  and  is  hence  equal  to  one  erg-per-second. 

2266.  The  unit  of  lieat  (sometimes  called  a  calorie) 
is  the  amount  of  heat  required  to  warm  one  gram  mass  of 
water  from  O''  to  1°  C. 

2267.  The  unit  of  electric-current  strength  is  a 

current  of  such  a  strength  that  when  passing  through  a  cir- 
cuit one  centimeter  in  length,  arranged  in  an  arc  having  a 
radius  of  one  centimeter,  it  will  exert  a  force  of  one  dyne  on 
a  unit  magnet  pole  placed  at  the  center.    (See  Art.  2379.) 

2268.  The  unit  of  quantity  of  an  electric  cur- 
rent is  that  quantity  which  is  conveyed  by  unit  current  in 
one  second. 

2269.  The  unit  of  difference  of  potential  (or  of 

electromotive  force)  is  defined  as  the  work  done  on  a 
unit  of  electricity  ;  hence  unit  difference  of  potential  exists 


ELECTRICITY  AND  MAGNETISM.  1477 

between  two  points  when  it  requires  the  expenditure  of  one 
erg  of  work  to  bring  a  unit  of  -\-  electricity  from  one  point 
to  the  other  against  the  electric  force. 

2270.  The  unit  of  resistance  is  that  resistance 
which  a  conductor  possesses  when  unit  difference  of  poten- 
tial between  its  two  ends  will  allow  a  current  of  unit 
strength  (that  is,  one  unit  of  quantity  per  second)  to  flow 
through  it. 

PRACTICAL,  UNITS. 

2271.  Several  of  the  above  absolute  units  would  be  in- 
conveniently large  and  others  inconveniently  small  for  prac- 
tical use.  The  following /r«(r/Z(f«/ units  have  therefore  been 
adopted  and  named  after  distinguished  men  of  science,  such 
as  Ampere,  Coulomb,  Volta,  Ohm,  Joule,  and  "Watt. 


THE   AMPERE. 

2272.  The  practical  unit  of  electric  current  is  the 
ampere.  The  ampere  is  smaller  than  the  absolute  unit  of 
current.     (Art.  2267.) 

1  absolute  unit  equals  10  amperes. 
1  ampere  equals  -^-^  absolute  unit. 

2273.  The  strength  of  an  electric  current  can  be  de- 
scribed as  a  quantity  of  electricity  flowing  continuously 
every  second,  or,  in  other  words,  it  is  the  rate  of  flow  of 
electricity,  just  as  the  current  expressed  in  gallons  per 
minute  is  the  rate  of  flow  in  liquids.  When  one  practical 
unit  quantity  of  electricity  is  flowing  every  second,  continu- 
ously, then  the  rate  of  flow  or  the  strength  of  the  current  is 
one  ampere ;  if  two  unit  quantities  are  flowing  continuously 
every  second,  then  the  strength  of  the  current  is  two 
amperes,  and  so  on.  It  makes  no  difference  in  the  number 
of  amperes  whether  the  current  flows  for  a  long  period  or 
for  only  a  fraction  of  a  second  ;  if  the  quantity  of  elec- 
tricity that  would  flow  in  one  second  is  the  same  in  both 
cases,  then  the  strength  of  current  in  amperes  is  the  same. 


1478  PRINCIPLES  OF 

2274.  Electricity  possesses  neither  weight  nor  exten- 
sion, and,  therefore,  an  electric  current  can  not  be  measured 
by  the  usual  methods  adopted  for  measuring  liquids  or 
gases.  In  liquids  the  strength  of  current  is  determined  by 
measuring  or  weighing  the  actual  quantity  of  the  liquid 
which  has  passed  between  two  points  in  a  certain  time  and 
dividing  the  result  by  the  time.  The  strength  of  an  elec- 
tric current,  on  the  contrary,  is  determined  directly  by  the 
effect  it  produces,  and  the  actual  quantity  of  electricity  which 
has  passed  between  two  points  in  a  certain  time  is  after- 
wards calculated  by  multiplying  the  strength  of  the  current 
by  the  time. 

The  principal  effects  produced  by  an  electric  current  are 
magnetic  attractions  and  repulsions,  chemical  decomposi- 
tion, and  heating  and  luminous  effects;  of  these,  the  two 
most  generally  used  for  measuring  are:  (1)  its  action  before 
a  magnetic  needle,  and  (2)  its  chemical  actions.  These 
methods  will  be  treated  upon  in  detail  in  the  section  on 
Electrical  Measurements  ;  the  following,  however,  will  give 
an  illustration  of  one  of  the  methods  used  in  measuring 
electric  currents,  and  also  one  mode  of  determining  the 
value  of  one  ampere  : 

2275.  A  current  of  electricity,  when  passing  through 
water,  decomposes  it  into  its  two  elements,  hydrogen  and 
oxygen.  The  quantity  of  water  decomposed  is  proportional 
to  the  strength  of  the  current  flowing,  and  also  to  the  time 
during  which  it  flows.  For  example,  if  a  current  of  two 
amperes  flowing  for  one  second  decomposes  a  certain 
quantity  of  water,  then  a  current  of  four  amperes  flowing 
for  one  second  will  decompose  txvice  that  quantity,  and  if  it 
flows  for  two  seconds  it  will  decompose  four  times  the 
original  quantity.  Consequently,  a  unit  strength  of  current 
can  be  conventionally  adopted  by  agreeing  that  it  is  that 
strength  of  current  which  will  decompose  a  certain  quantity 
of  water  in  a  certain  time,  and  agreeing  furthermore  upon 
the  quantity  of  water  and  the  time. 


ELECTRICITY  AND  MAGNETISM.  1479 

2276.  By  universal  agreement,  one  ampere  is  that 
strength  of  current  which  will  decompose  .00009324  gram 
or  .0014388  grain  of  water  in  one  second. 

Rule. —  To  find  the  strength  of  an  electric  current  in 
amperes  by  the  decomposition  of  water ^  divide  the  weight  of 
the  quantity  of  water  decomposed  by  the  tiuie  in  seconds  re- 
quired to  decompose  it ;  if  the  mass  of  water  is  expressed  in 
grams ^  divide  tJie  quotient  by  .0000982^;  bnt  if  expressed  in 
grains,  divide  by  .OOlJi.388. 

Let  W  =  weight  of  water  decomposed  in  grams  ; 
w  =  weight  of  water  decomposed  in  grains  ; 
/    =  time  in  seconds  required  for  decomposition  ; 
C   =  current  in  amperes. 
Then  the  strength  of  the  current  in  amperes  is  given  by 
the  formulas: 

~  tx  .00009324*  V"*^!*) 

^""/X.  0014388-  (402.) 

2277.     Rule. — To  find  the  quantity  of  ivater  zvJiich  an 
electric  current  of  a  given  strength  can  decompose  in  a  given 
time,  multiply  the  strength  of  the  current  in  amperes  by  the 
time  in   seconds   during  which   the  current  fiows ;    if  the 
quantity  of  water  is  to  be  expressed  in  grams,  multiply  the 
product  by  .  0000932^  ;  but  if  in  grains,  multiply  by  .  0011^388. 
Let  q  =:  quantity  of  water  in  grams  ; 
q'  =  quantity  of  water  in  grains  ; 
t  =  time  in  seconds  of  cui  rent  flow  ; 
C  =  current  in  amperes. 
Then  the  quantity  of  water  which  can  be  decomposed  by 
a  current  of  C  amperes  in  /  seconds  is  given  by  the  for- 
mulas: 

^  =  .00009324  6'/.  (403.) 

q'  =  .0014388  C  t.  (404.) 

Example. — The  current  from  a  voltaic  cell  decomposes  ivater  at  the 
rate  of  1.29493  grains  per  hour  ;  what  is  the  strength  of  current  in 
amperes  ? 


1480  PRINCIPLES  OP 

Solution. —    1  hour  =  3,600  seconds.  By  formula  403,  the  strength 

of  current 

_  1.29492         _ 

^-3,600  X  .0014388  "  '^^  ^^V^^^'     ^^S" 

Example. — Find  the  number  of  grains  of  water  decomposed  in 
8  hours  by  a  current  of  .6  ampere. 

Solution. —    3   hours  =  10,800   seconds.      By   formula   404,   the 
quantity  of  water  decomposed 

g'  =  .0014388  X  .6  X  10,800  =  9.3234  grains.     Ans. 


THE  COULOMB. 

2278.  The  practical  unit  of  quantity  of  an  electric 
current  is  the  coulomb. 

The  coulomb  is  smaller  than  the  absolute  unit  of  quantity 
of  current.     (Art.  2268.) 

1  absolute  unit  equals  10  coulombs. 
1  coulomb  equals  ^^  absolute  unit. 

2279.  Relation  of  Atapere  and  Coulomb. — The 

relation  of  the  ampere  and  the  coulomb  may  be  made  clear 
by  the  water-flow  analogy  : 

W/ien  a  current  of  water  Jlows  tJirough  a  pipe,  then  the 
current  must  have  a  certain  fixed  strength,  if  a  definite 
quantity  of  water  is  to  be  delivered  at  any  point  in  a  given 
time. 

When  a  current  of  electricity  flows  tJirough  a  conductor, 
then  the  ciLrrent  must  have  a  certain  fixed  ampere  strength, 
if  a  definite  number  of  coulombs  of  current  is  to  be  delivered 
at  any  point  in  a  given  time. 

2280.  The  coulomb  may  be  further  defined  as  being  such 
a  quantity  of  electricity  as  zvould pass  in  one  second  tJirough 
a  circuit  in  zvJiich  the  strength  of  the  current  is  one  ampere. 

One  coulomb  delivered  per  second  therefore  represents  a 
current  of  one  ampere. 

One  ampere  fioiving  for  one  second  zvill  deliver  one  coulomb. 

j2281.     If  ^  =  quantity  of  electricity  in  coulombs  ; 
C  —-  strength  of  current  in  amperes; 
/  =  time  in  seconds. 


ELECTRICITY  AND  MAGNETISM.  1481 

then,  Q  =  Ct.  (405.) 

By  transposition,    C  ■=■—  and  t  —  -^. 

Example. — Find  the  quantity  of  electricity  in  coulombs  that  flows 
around  a  circuit  in  \\  hours,  when  the  strength  of  current  is  12  amperes. 
Solution. — By  formula  405,  the  quantity  of  electricity 
^  =  C/  =  12  >.  1.5  X  3,600  =  64,800  coulombs.     Ans. 


EXAMPLES  FOR  PRACTICE. 

1.  Find  the  quantity  of  electricity  in  coulombs  that  passes  in  a 
circuit  in  which  a  current  of  40  amperes  flows  for  55  seconds. 

Ans.  2,200  coulombs. 

2.  Find  the  quantity  of  electricity  in  coulombs  that  passes  in  a 
circuit  in  which  a  current  of  13  amperes  flows  for  15  minutes. 

Ans.  11,700  coulombs. 

3.  36,000  coulombs  of  electricity  pass  through  a  closed  circuit  in 
1  hour.  If  the  flow  is  uniform  during  that  time,  what  is  the  strength 
of  the  current  ?  Ans.  10  amperes. 

4.  How  long  will  it  take  72,000  coulombs  of  electricity  to  pass  in 
a  circuit  in  which  the  strength  of  current  is  4  amperes  ?    Ans.  5  hours. 


THE  OHM. 

2282.  The  practical  unit  of  resistance  is  the  ohim. 
The  ohm  is  greater  than  the  absolute  unit  of  resistance. 

(Art.  2270.) 

1  absolute  unit  equals  one-billionth  (i  r.r.r.  nnri  nnn)  ^^  **^ 

ohm. 

1  ohm  equals  1  billion  (1,000,000,000)  absolute  units. 

2283.  The  ohm  is  the  only  unit  in  electrical  measure- 
ments for  which  a  material  standard  can  be  adopted.  The 
basis  of  any  system  of  physical  measurements  is  generally 
some  material  standard  conventionally  adopted  as  the  unit; 
physical  measurements  in  each  system  are  made  by  compari- 
son with  the  unit  of  that  system. 

As  a  basis  for  the  measurement  of  resistance,  Siemens 
originally  proposed  a  column  of  mercury  having  a  height  of 
100  centimeters  and  a  cross-section  of  one  square  millimeter, 
at  the  temperature  of  0°  C. ;  that  is,  at  the  temperature  of 


1482 


PRINCIPLES  OF 


freezing  water.     This  column  of  mercury  he  claimed  had  a 
resistance  of  one  ohm. 

2284.  The  idea  of  utilizing  a  column  of  mercury  of 
1  square  millimeter  cross-section  at  0°  C.  as  the  practical 
unit  of  resistance  has  been  universally  adopted,  but  the 
height  of  this  column  has  never  been  exactly  determined. 
There  are,  therefore,  various  values  of  the  unit  often  found 
quoted.  The  following  list  gives  these  various  values  in 
tabular  form  with  annotations  denoting  their  use. 


TABLE  75. 
VARIOUS  VALUES  OF  THE  OHM. 


Name. 

Height  of 

Mercury 

Column. 

Cross-Sec- 
tion of 
Mercury 
Column. 

Use. 

Siemens'   Unit.  . 

100  cm. 

1  sq.  mm. 

Out  of  use,  because 
incorrect. 

British    Associa- 

tion Unit,  writ- 

ten B.  A.  U. .  . 

104.8  cm. 

1  sq    mm. 

Out  of  use,  because 
incorrect. 

Legal  Ohm  (com- 

monly     called 

Ohm) 

106.0  cm. 

1  sq.  mm. 

In  all  technical  meas- 
urements and  cal- 
culations, as  well 
as  in  this  Course. 

International 

Ohm .  - 

106.3  cm. 

1  sq.  mm. 

Latest  and  most  ex- 

act determination. 

Correct  within---—— 
0,000 

part. 

Not    yet    in    general 

use. 

ELECTRICITY  AND  MAGNETISM.  1483 

2285.  The  relative  values  of  these  units  are  given  by 
the  following  list: 

1  legal  ohm         =  1.0112  B.  A.  U. 

1  legal  ohm         =  1.0600  Siemens'  Unit. 

1  B.  A.  U.  =    .9889  legal  ohm. 

1  B.  A.  U.  =  1.0483  Siemens'  Unit. 

1  Siemens'  Unit  =    .9540  B.  A.  U. 

1  Siemens'  Unit  =    .9434  legal  ohm. 

2286.  As  stated  in  Table  75,  the  legal  ohm,  commonly 
called  the  otun,  is  used  as  yet  in  all  technical  measure- 
ments and  throughout  this  Course,  so  that  when  the  ohm  is 
mentioned  we  understand  thereby  the  resistance  of  a  column 
of  mercury  106  cm.  (or  41.7323  inches)  high,  having  a  cross- 
section  of  1  sq.  mm.  (or  .00155  sq.  in.)  at  0°  C.  (or  32°  F.). 

2287.  It  very  often  occurs  in  practical  work  that  ex- 
ceedingly small  resistances  are  to  be  measured,  for  which 
the  ohm  as  a  unit  causes  unnecessary  labor,  because  so 
very  large.  The  absolute  unit  of  resistance,  on  the  other 
hand,  is  too  small  to  do  very  well.  Therefore,  to  facilitate 
calculations  and  measurements,  a  unit  is  used  for  such  work 

having  the  value  of  one-millionth  |  nPtc^)  ^^  ^^  ohm. 

2288.  This  derived  practical  unit  is  called  the  tnicroliin. 
Therefore,  to  express  the  resistance  in  microhms^  multiply 
the  resistance  in  ohms  by  1,000,000;  and,  conversely,  to  ex- 
press the  resistance  in  ohms,  divide  the  resistance  in  inicroJims 
by  1,000,000.     For  example,   .75  ohm  =  .75  X  1,000,000  = 

750,000  microhms,  or  750,000  microhms  =  .'^q^qq^O  ^  '"^^ 
ohm. 

2289.  Another  similarly  derived  practical  unit  is  the 
tnegoliin,  devised  to  facilitate  calculations  and  measure- 
ments of  exceedingly  large  resistances,  and  is  equal  to  1,000,- 
000  ohms.  Therefore,  to  express  the  resistance  in  megohms^ 
divide  the  resistance  in  ohms  by  1,000,000;  and,  conversely. 


1484  PRINCIPLES  OF 

to  express  the  resistance  in  ohms,  multiply  the  resistance  in 

megohms  by  1,000,000. 

T.  1      o.^  ^^^    ,  850,000  „,  , 

For  example,  850,000  ohms  =  ■  =  .85  megohm,  or 

.85  megohm  =  .85  X  1,000,000  =  850,000  ohms. 

The  megohm  is  used  mainly  in  the  determination  of  ths 
resistance  of  non-conductors  and  insulators. 


EXAMPLES  FOR  PRACTICE. 

1.  Give  the  equivalent  resistance  in  microhms  of  .00425  ohm. 

Ans.  4,250  microhms. 

2.  Give  the  equivalent  resistance  in  ohms  of  375  microhms. 

Ans.    .000375  ohm. 

8.     Give  the  equivalent  resistance  in  megohms  of  4,560,000  ohms. 

Ans.  4.56  megohms. 

4.     Give  the  equivalent  resistance  in  ohms  of  63.5  megohms. 

Ans.  62,500,000  ohms. 


RESISTANCE. 

2290.  The  resistance  which  all  substances  offer  to  the 
passage  of  an  electric  current  is  one  of  the  most  important 
quantities  in  electrical  measurements.  Resistance  is  that 
attribute  of  a  conductor  or  of  a  circuit  which  determines  the 
strength  of  the  electric  current  that  can  be  sent  through 
the  conductor  or  the  circuit,  around  which  a  constant  differ- 
ence of  potential  is  maintained,  as  shown  by  Ohm's  law, 
Art.  2253. 

2291 .  If  a  given  conductor  offers  a  resistance  of  2  ohms 
to  a  current  of  1  ampere,  it  offers  the  same  amount,  no  more 
nor  no  less,  to  a  current  of  10  amperes.     Hence  we  have  the 

Rule. —  TJie  resistance  of  a  given  conductor  is  ahvays  con- 
stant at  the  same  temperature^  irrespective  of  the  strength  of 
current  fiovoing  through  it  or  the  electromotive  force  of  the 
current. 

2292.  When  it  is  required  to  find  the  resistance  of  a 
conductor  of  which  the  length  is  varied,  though  all  other 


ELECTRICITY  AND  MAGNETISM.  1485 

conditions  remain  unchanged,   the  following-  formula  may 
be  used  : 

r,  :r,  ::/,:/„  or  r,  =  '^^  (406.) 

In  this  formula, 

r,  =  the  original  resistance ; 

r,  =  the  required  or  changed  resistance; 

/j  =  the  original  length; 

/^  =  the  changed  length. 

2293.  As  in  all  examples  of  proportion,  the  two  lengths 
must  be  reduced  to  the  same  unit.     We  then  have  the 

Rule. —  TJie  resistance  of  a  given  conductor  increases  as 
the  lengtJi  of  the  conductor  increases ;  that  is,  the  resistance 
of  a  conductor  is  directly  proportional  to  its  length. 

Example. — Find  the  resistance  of  1  mile  of  copper  wire,  if  the 

resistance  of  10  feet  of  the  same  wire  is  .013  ohm. 

Solution. —    rx  =  .013  ohm ;  /i=  10  feet,  and  h=  1  mile  =  5,280  feet 

Then,  by  formula  406,  the  required  resistance 

.013x5,280      coc^A    X.  A 

^3  = ^^ =  6.864  ohms.     Ans. 

Example. — Find  the  resistance  of  11  in.  of  a  German  silver  wire,  if 
the  resistance  of  100  feet  of  the  same  wire  is  2.4  ohms. 

Solution.—    i\  =  2.4  ohms  ;  A  =  100  X  13  =  1,200  in. ;  /»  =  11  in. 
By  formula  406,  the  required  resistance 


EXAMPLES  FOR  PRACTICE. 

2294,  1.  Find  the  resistance  per  foot  of  a  wire,  if  the  resist- 
ance of  1  mile  of  the  wire  is  14.75  ohms.  Ans.  .002793  ohm. 

2.  If  the  resistance  of  18  in.  of  a  certain  piece  of  wire  is  .027  ohm, 
what  is  the  resistance  of  1,020  feet  of  the  same  wire  ?    Ans.  18.36  ohms. 


2295.  If  the  sectional  area  of  a  conductor  is  increased, 
and  other  conditions  remain  unchanged,  the  resistance  of 
the  conductor  will  be  decreased.  For  instance,  if  the  sec- 
tional area  be  doubled  the  resistance  is  halved,  and,  con- 
versely, if  the  sectional  area  is  halved  the  resistance  is 
doubled.      The  resistance  of  a  conductor,  therefore,  grows 


1486  PRINCIPLES  OF 

with  decreasing  sectional  area,  and  diminishes  with  increas- 
ing sectional  area.  This  may  be  expressed  by  the  general 
rule : 

2296.  Rule. —  The  resistance  of  a  conductor  varies  in- 
versely as  its  sectional  area. 

The  value  of  the  resistance  of  a  conductor  for  any  change 
in  its  sectional  area  may  be  obtained  from  the  following 
formula  : 

r,  :  r,  ::«,:«,,  or  r,  =  ^.  (407.) 

In  this  formula, 

r^  =  the  original  resistance ; 
r,  =  the  required  resistance ; 
a  =  the  original  sectional  area ; 
a^  =  the  changed  sectional  area. 

Example. — The  resistance  of  a  conductor  whose  sectional  area  is 
.025  sq.  in.  is  .32  ohm  ;  what  would  be  the  resistance  of  the  conductor 
if  its  sectional  area  were  increased  to  .125  sq.  in.,  other  conditions 
remaining  unchanged  ? 

Solution. —    r,  =  .32  ohm;  ^i=:.025  sq.  in.,  and  «a  =  .125  sq.  in. 
Then,  by  formula  407,  the  required  resistance 
.32  X  .025 


rs  =  ' 


.125 


=  .064  ohm.     Ans. 


Example. — The  sectional  area  of  a  conductor  is  .01  sq.  in.  and  its 
resistance  is  1  ohm  ;  if  its  sectional  area  is  decreased  to  .001  sq.  in.,  and 
other  conditions  remain  unchanged,  what  will  be  its  resistance  ? 

Solution. —  r,  ~  1  ohm  ;  ax  =  .01  sq.  in.,  and  a^  =  .001  sq.  in. 
By  formula  407,  the  required  resistance 

^  =  1^^  =  10  ohms.     Ans. 
.001 

2297.  The  resistance  of  a  conductor  is  independent  of 
the  shape  of  its  cross-section.  For  example,  this  cross- 
section  may  be  of  circular,  square,  rectangular,  or  irregular 
shape;  if  the  sectional  area  is  the  same  in  all  cases,  the 
resistances  will  be  the  same,  other  conditions  being  similar. 
When  comparing  the  resistances  of  copper  wires  of  circular 
cross-section,  it  is  usually  simpler  to  express  the  copper  wire 


ELECTRICITY  AND  MAGNETISM.  148? 

by  its  diameter  than  by  its  area.  The  sectional  area  of  any 
circular  cross-section  is,  however,  proportional  to  the  square 
of  the  diameter;  for  the  sectional  area  =  diameter'*  X  .7854. 
We  therefore  have  the  rule: 

2298.     TJie  resistance  of  a  conductor  of  circular  cross- 
section  is  inversely  proportio7tal  to  the  square  of  its  diameter. 
Formula  407  may,  therefore,  be  rewritten  as  follows: 

r,  :  r,  ::  d^  :  D\  or  r,  =  ^^.  (408.) 

In  this  formula, 

r,  =  the  original  resistance ; 
r^  =  the  required  resistance; 
£}  =  the  original  diameter; 
d  =  the  changed  diameter. 

Example. — The  resistance  of  a  round  copper  wire  .12  in.  in  diame- 
ter is  .64  ohm  ;  find  the  resistance  of  the  conductor  when  its  diameter 
is  increased  to  .24  in.,  the  other  conditions  remaining  unchanged. 

Solution. —    n  =  .64  ohm  ;  Z>  =  .12  in.,  and  d=  .24  in. 

Then,  by  formula  408,  the  required  resistance 

.64  X  .12^ 
r2  =  '- ^, — •  =  .16  ohm.     Ans. 

Example. — The  diameter  of  a  round  wire  is  .1  in.  and  its  resistance 
is  2  ohms  ;  what  would  be  its  resistance  if  its  diameter  were  decreased 
to  .02  in.,  and  the  other  conditions  remained  unchanged  ? 

Solution. —    ri  =  2  ohms  ;  D  =  .1  in.,  and  il=  .02  in. 

By  formula  408,  the  required  resistance 

2x.l^      2X.01      ^^    ^ 


EXAMPLES  FOR   PRACTICE^ 

The  resistance  of  a  piece  of  round  copper  wire  .001  in.  in  diameter 
and  1  foot  long  is  10.8  ohms  ;  use  the  same  quality  of  copper,  and 
solve  the  following  problems  : 

1.  Find  the  resistance  of  1,200  feet  of  round  copper  wire  .102  in.  in 
diameter.  Ans.  1.2457  ohms, 

2.  Find  the  resistance  of  1  mile  of  round  copper  ^  in.  in  diameter. 

Ans.  3.6495  ohms. 

3.  Find  the  resistance  of  1,500  feet  of  square  copper  wire  .1  in.  on  a 
side.  Ans,  1,3723  ohma 


1488  PRINCIPLES  OF 

4.  Find  the  resistance  of  100  yards  of  copper  wire  .12  in.  wide  by  .09 
in.  thick.  Ans.  .23562  ohm. 

Note. — The  temperature  of  the  copper  in  all  the  above  problems  is 
assumed  to  be  equal.  

2299.  The  Resistance  of  Metals. — It  was  stated  in 
Art.  2216  that  the  resistance  varies  in  different  sub- 
stances; that  is,  one  substance  offers  a  higher  resistance  to 
a  current  of  electricity  than  another.  In  order  to  compare 
the  resistances  of  different  substances,  however,  the  dimen- 
sions of  the  pieces  to  be  measured  must  be  equal.  For,  by- 
changing  its  dimensions,  a  good  conductor  may  be  made  to 
offer  the  same  resistance  as  an  inferior  one.  Under  like 
conditions,  annealed  silver  offers  the  least  resistance  of 
all  known  metals  or  conductors.  Soft  annealed  copper 
comes  next  on  the  list,  and  then  follow  all  other  metals  and 
conductors. 

2300.  The  resistance  of  a  given  conductor,  however, 
is  not  always  constant;  it  changes  with  the  temperature, 
and  also  with  the  physical  condition  of  the  conductor.  In 
all  metals  the  resistance  increases  as  the  temperature  rises; 
in  liquids  and  carbons  the  resistance  decreases  as  the  tem- 
perature rises;  and  in  non-conductors  the  resistance  de- 
creases as  the  temperature  rises.  The  amount  of  variation 
in  the  resistance  caused  by  a  change  in  temperature  will  be 
treated  upon  under  Electrical  Measurements;  it  is  a  small 
factor,  and  can  be  neglected  for  the  present. 

2301.  A  list  of  the  common  metals  is  given  in  Table  76 
in  the  order  of  their  relative  resistances,  beginning  with 
silver  as  offering  the  least  resistance.  The  first  column  of 
figures  gives  the  actual  resistance  in  microluns  of  1  cubic 
inch  of  the  corresponding  metal  at  32°  Fahrenheit,  or  the 
freezing-point  of  water.  By  the  resistance  of  1  cubic  inch 
is  meant  the  resistance  of  a  piece  of  the  conductor,  the 
length  of  which  is  1  inch,  and  whose  sectional  area  is  1  sq. 
in.  Therefore,  the  resistance  of  any  conductor  of  known 
dimensions  which  is  made  of  one  of  the  metals  in  the  list 
can  be  determined  by  applying  the  formulas  in  Arts.  2296 


ELECTRICITY  AND  MAGNETISM. 


1489 


and  2298.  The  second  column  of  figures  gives  the  rela- 
tive resistances  of  the  different  metals  compared  with  silver. 
For  example,  the  resistance  of  mercury  is  62.73  times  the 
resistance  of  silver,  or  the  resistance  of  iron  is  6,46  times 
the  resistance  of  silver. 

TABLE  76. 


Name  of  Metal. 

Resistance 

in  Microhms 

of  1  Cu.  In. 

at  33°  F. 

Relative 
Resistance. 

Silver,  annealed 

.5921 

.6292 

.6433 

.6433 

.8102 

.8247 

1.1470 

2.2150 

3.5650 

3.8250 

4.9070 

5.2020 

7.7280 

8.2400 

13.9800 

37.1500 

51.6500 

1.000 

Copper,  annealed 

1.063 

Silver   hard  drawn 

1.086 

Copper   hard  drawn 

1.086 

Gold    annealed 

L369 

Gold,  hard  drawn 

1.393 

Aluminum,  annealed 

1.935 

Zinc   pressed 

3.741 

Platinum    annealed 

6.022 

Iron   annealed 

6.460 

Nickel    annealed 

8.285 

Tin,  pressed 

8.784 

Lead,  pressed 

13.050 

German  Silver 

13.920 

Antimony,  pressed 

Mercury 

23.600 
62.730 

Bismuth,  pressed 

87.230 

EXAMPLES  FOR   PRACTICE. 

1.  Find  the  resistance   in  ohms  of  a  round  column  of   mercury 
70  inches  high  and  .05  inch  in  diameter.  Ans.  1.3244  ohms. 

2.  Find  the  resistance  in  ohms  of   1,000   feet  of  round   German 
silver  wire  .2  inch  in  diameter.  Ans.  8. 1476  ohms. 

3.  Find  the  resistance  in  microhms  of  a  cubic  foot  of  bismuth, 
pressed.  Ans.  4.3042  microhms. 

4.  Find  the  resistance  in  ohms  of  1  mile  of  square  iron  wire  (an- 
nealed) .  1  inch  on  a  side.  Ans.  34. 2353  ohms. 


1490  PRINCIPLES  OF 

2302.  In  a  simple  voltaic  cell,  the  intei'nal  resistance, 
that  is,  the  resistance  of  the  two  plates  and  the  electrolyte, 
is  of  great  importance,  for  it  determines  the  maximum 
strength  of  current  that  can  possibly  be  obtained  from  the 
cell.  In  the  common  forms  of  cells,  the  internal  resistance 
may  be  excessively  large,  owing  to  the  resistance  of  the  elec- 
trolyte, the  relative  resistance  of  ordinary  liquids  used  as  elec- 
trolytes being  from  1  to  20  million  times  that  of  the  common 
metals.  In  liquids,  as  in  all  conductors,  the  resistance  in- 
creases as  the  length  of  the  circuit  increases,  and  diminishes 
as  its  sectional  area  increases.  Consequently,  the  internal 
resistance  of  a  simple  voltaic  cell  is  reduced  by  decreasing 
the  distance  between  the  two  plates  or  elements  and  by 
increasing  their  active  surfaces. 

The  internal  resistance  of  the  ordinary  forms  of  cells 
varies  from  about  .2  to  20  ohms. 


THE  VOLT. 

2303.  The  practical  unit  of  electromotive  force,  or 
difference  of  potential,  is  the  volt. 

The  volt  is  greater  than  the  absolute  unit  of  electromo- 
tive force.     (Art.  2269.) 

1     absolute     unit     equals      one     one-hundred-millionths 


(■ -I  of  a  volt. 
100,000,000/ 


1  volt  equals  one  hundred  million  (100,000,000)  absolute 
units. 

2304.  The  volt  may  be  further  defined  as  being  that 
E.  M.  F.  %vJiicJi  will  cause  a  current  of  one  ampere  to  flozv 
against  the  resistance  of  one  ohm. 

2305.  The  volt  is  the  measure  of  the  electromotive 
force,  which  has  been  defined  and  explained  in  Arts.  2242 
and  2252. 

The  various  terms  electromotive  force,  pressure, 
difference  of  potential,  and  voltage  are,  in  general, 
used  to  signify  the   same   thing;  namely,  that  force  which 


ELECTRICITY  AND  MAGNETISM.  1491 

tends  to  move  a  current  of  electricity  against  the  resistance 
of  a  conductor. 

2306.  The  maximum  difference  of  potential  developed 
by  any  voltaic  couple  (see  Art.  2243)  placed  in  any  electro- 
lyte is  about  2.25  volts  ;  in  the  common  forms  of  cells,  the 
difference  of  potential  developed  averages  from  .75  to  1.75 
volts. 

2307.  The  determination  of  the  value  of  the  E.  M.  F. 

in  any  circuit  is  made  by  applying  Ohm's  law  (see  Art. 
2253),  which  gives  the  E.  M.  F.  accurately  when  the  re- 
sistance and  current  are  known.  Measuring  instruments, 
which  will  be  described  under  Electrical  Measurements, 
have  been  devised  upon  the  principle  of  Ohm's  law,  to 
indicate  the  E.  M.  F.  directly. 


OHM'S  LAT^  APPLIED  TO  CLOSED  CIRCUITS. 

2308.  Ohm's  law,  as  shown  in  Art.  2253,  expresses 
the  relation  between  the  three  fundamental  units  of  resist- 
ance, electrical  pressure,  and  current.  If  any  two  of  these 
values  are  known,  the  third  is  found  by  solving  the  simple 
equation  of  their  relation.  Before  applying  this  law,  how- 
ever, the  following  four  facts  should  be  carefully  noted  : 

2309.  I. — TJie  strength  of  a  current  (C)  is  the  same  in 
all  parts  of  a  closed  circuit,  except  in  the  case  of  divided 
circuits. 

II.- — In  the  case  of  a  divided  circuit,  the  sum  of  the  cur- 
rents  in  the  separate  brandies  is  ahvays  equal  to  the  current 
in  the  main  or  undivided  circuit. 

III. —  TJie  resistance  {R)  is  the  total  resistance  of  the  cir- 
cuit, that  is,  the  sum  of  the  resistances  of  the  internal  circuit 
and  of  the  external  circuit,  or  its  equivalent. 

IV. —  The  electromotive  force  (E)  in  a  closed  circuit  is  the 
total  generated  difference  of  potential  in  that  circuit. 

The  law  may  now  be  stated  by  the  following  rules  and 
formulas : 


1493  PRINCIPLES  OF 

23  lO.  Rule  I. —  The  strength  in  amperes  of  a  current 
{C)  flowing  in  a  closed  circuity  when  the  electromotive  force 
{E)  and  the  total  resistance  (R)  are  knozvn,  is  found  by  divi- 
ding the  electromotive  force  in  volts  by  the  total  resistance  in 
ohms ;  that  is, 

^  electromotive  force  ^      E  ,  ^^^  . 

Current  =  ■ r— ,  or  C  =-^-  (409.) 

resistance  K  ^ 

Rule  II. —  The  total  resistance  (R)  in  ohms  of  a  closed  cir- 
cuit, IV hen  the  electromotive  force  {E)  and  the  current  {C) 
are  known,  is  found  by  dividing  the  electromotive  force  in 
volts  by  the  current  in  amperes ;  that  is, 

_.     .  electromotive  force  „       E  /  ^  ^  ^  \ 

Resistance  =  • ,  or  R  =—;;,.         (41 0.) 

current  6 

Rule    III. —  The   total  electromotive  force  [E)    in   volts 
developed  in  a  closed  circuit,  when  the  current  (C)  and  the 
total  resistance  (R)  are  known,  is  found  by  multiplying  the 
current  in  amperes  by  the  total  resistance  in  ohms  ;  that  is^ 
Electromotive  force  =  current  X  resistance,  or 
E  =  CR.  (411.) 

2311.  The  following  examples  show  the  application  of 
Ohm's  law  as  given  by  the  formulas  of  the  preceding 
article: 

Example. — What  current  can  be  made  to  flow  through  a  circuit 
having  a  resistance  of  10  ohms,  if  an  E.  M.  F.  of  100  volts  is  applied  ? 

Solution. —  ^=100;  i?  =  10  ;  hence,  by  formula  409,  the  re- 
quired current 

C  =  -jTT-  =  10  amperes.     Ans. 

Example. — What  resistance  can  be  overcome  by  a  current  of  50 
amperes,  if  the  electromotive  force  is  500  volts  ? 

Solution. —  (7=  50;  -£"=  500;  hence,  by  formula  41 0,  the  required 
resistance 

R  =:-=7r  —  10  ohms.     Ans. 
50 

Example. — What  voltage  is  required  to  send  a  current  of  25  amperes 

through  a  resistance  of  4  ohms  ? 

Solution. —    C=  25  ;  i?  =  4  ;  hence,  by  formula  41 1,  the  required 

voltage 

J?  =  25  X  4  =  100  volts.     Ans. 


ELECTRICITY  AND  MAGNETISM.  1493 

Example. — The  two  electrodes  of  a  simple  voltaic  cell  are  connected 
together  by  a  copper  wire,  the  resistance  of  which  is  1  ohm.  If  the 
internal  resistance  of  the  cell  is  4  ohms  and  the  electromotive  force 
developed  is  3  volts,  what  is  the  strength  of  the  current  in  the  circuit  ? 

Solution. — Let  r,  =  the  internal  resistance  and  re  —  the  external 
resistance ;  that  is,  the  resistance  of  the  copper  wire.     Then, 

i?  =  r,  +  re  =  4  +  1  =  5. 
By  formula  409,  the  current 

E     2 
C=  -n  =  k"=  •■^  ampere  flowing  through  the  circuit.     Ans. 

Example. — The  total  electromotive  force  developed  in  a  closed 
circuit  is  1.2  volts  and  the  strength  of  the  current  flowing  is  .3  ampere  ; 
find  the  total  resistance  of  the  circuit. 

Solution. — By  formula  410, 

R  =  — ^  =  4  ohms.     Ans. 

.  o 

Example. — The  internal  resistance  of  a  certain  dynamo-electric 
machine  is  10.9  ohms  and  the  external  resistance  is  73  ohms  ;  the 
voltage  of  the  machine  is  839  volts.  Find  the  strength  of  the  current 
flowing  in  the  circuit. 

Solution.—  n  =  10.9  ;  r^  =  73  ;  J?  =  10.9  +  73  =  83.9,  By  formula 
409, 

C  —  ^^  =  10  amperes.     Ans. 


EXAMPLES  FOR  PRACTICE. 

1.  The  current  from  a  simple  voltaic  cell  decomposes  water  at  the 
rate  of  2.58984  grains  per  hour,  and  the  total  resistance  of  the  circuit 
through  which  the  current  flows  is  2  ohms.  Find  («)  the  strength  of 
the  current,  and  {b)  the  total  electromotive  force  developed  by  the  cell. 

j  (a)  .5  ampere. 
^^^•\(b)   Ivolt. 

2.  A  battery  of  10  cells  connected  in  series  generates  a  total  elec- 
tromotive force  of  12  volts.  If  the  resistance  of  each  cell  is  4  ohms 
and  the  resistance  of  an  external  circuit  is  8  ohms,  what  is  the  strength 
of  current  flowing  in  the  circuit  ?  Ans.  .25  ampere. 

3.  Given, 

Internal    resistance  =  4  ohms. 
Electromotive  force  =  1.5  volts. 
Current  =  .2  ampere. 
Find  the  external  resistance.  Ans.  3.5  ohms. 


1494 


PRINCIPLES  OF 


4.  Given. 

Electromotive  force  =  24  volts. 

Current  =  .6  ampere. 
If  the  external  resistance  is  3  times  the  internal,  what  is  the  resistance 
of  each?  a^^    i  External,  30  ohms. 

Internal     10  ohms. 


Ans. 


DROP   OF  POTENTIAL. 

2312.  Referring  again  to  the  flow  of  water  in  pipes, 
we  may  tabulate  the  analogies  as  given  in  Table  77,  a  care- 
ful study  of  which  will  do  much  to  assist  the  understanding 
of  what  is  to  follow. 

2313.  The  fourth  analogy  of  the  table  states  that 
the  loss  of  pressure  or  E.  M.  F.,  due  to  the  resistance 
of  conductor,  is  termed  drop  of  potential.  This  drop 
may  be  made  clearer  by  the  following  : 

Let  Fig.  913  represent  a  tank  T  of  water  with  a  hori- 
zontal discharge-pipe  E  JV,  which  is  provided  with    open 


,  Fig.  913. 

vertical  tubes  at  a,  b,  c,  etc.  If  the  outlet  at  N  is  closed 
the  water  in  the  vertical  tubes  will  rise  to  the  height  of  the 
water  in  the  tank  ;  but  if  the  water  is  allowed  to  flow  freely 
from  the  outlet  at  N,  then  the  height  of  the  water  in  the 
tubes  will  be  represented  by  the  inclined  line  at  a',  b\  c' , 
etc.  The  pressure  or  licad  of  the  water,  which  is  measured 
by  the  height  of  the  water  in  the  tubes,  decreases  in  the 
direction  in  which  the  water  is  flowing,  so  that  the  water 
which  leaves  the  discharge  outlet  at  N  has  considerably  less 
pressure  than  the  water  entering  at  E. 


ELECTRICITY  AND  MAGNETISM. 


1495 


TABLE  77. 

A1VAI.OGIES  BETWEEN   THE  FLOW^  OF  TVATER  AJVD 
ELECTRICITY. 


Water  in  Pipes. 


Electricity  in  Conductors. 


I. 


XL 


III. 


IV. 


V. 


VI. 


Difference  of  level  tends 
to  make  water  fall 
from  the  upper  level 
to  the  lower  level. 

Difference        of      level 
hence  acts  as  a  pres 
sure  tending  to  cause 
a  flow. 

If  not  entirely  obstruct 
ed,   this  pressure  ac- 
tually produces  a  flow 
of  water. 

Some  of  this  pressure  is 
lost  by  friction  of  the 
water  against  inside 
walls  of  pipe. 

This  loss  by  friction  is 
directly  proportional 
to  the  length  of  the 
pipe,  and  inversely 
proportional  to  the 
diameter  of  the  pipe. 

No  quantity  of  water 
can  flow  through  a 
pipe  without  suffering 
some  loss  in  this  man- 
ner; in  other  words 
there  is  no  such  thing 
as  an  absolutely  fric 
tionless  pipe. 


Difference  of  potential  tends 
to  make  electric  current 
fall  from  point  of  high  po- 
tential to  point  of  low  po- 
tential. 

Difference  of  potential  or 
E.  M.  F.,  hence  acts  as  a 
pressure  tending  to  cause 
a  flow- 

If  not  entirely  obstructed, 
this  pressure  or  E.  M.  F. 
actually  produces  a  flow  of 
current. 

Some  of  this  pressure  is  lost 
by  the  electrical  resistance 
of  the  conductor.  The  loss 
is  called  di'op  of  potential. 

This  loss  or  drop  due  to  re- 
sistance is  directly  propor- 
tional to  the  length  of  the 
conductor,  and  inversely 
proportional  to  its  area  of 
cross-section. 

No  quantity  of  electricity 
can  flow  through  a  con- 
ductor without  suffering 
some  loss  in  this  manner  ; 
in  other  words,  there  is  no 
such  thing  as  an  absolutely 
resistanceless  conductor. 


1496 


PRINCIPLES  OP 


2314.  The  same  action  takes  place  in  a  current  of 
electricity  flowing  along  a  conductor,  and  can  also  be 
graphically  shown.  In  Fig.  914,  B  represents  a  voltaic 
battery  with  the  negative  electrode  connected  directly  to 
the  earth  at  E^  and  the  positive  electrode  to  a  long  con- 
ductor A  L,  which  is  also  connected  to  the  earth  at  E'. 
The  battery  may  be  regarded  as  a  machine  which  raises  the 
pressure  or  potential  of  electricity  from  zero  (or  that  of  the 
earth)  to  a  height  equal  to  the  distance  a  a';  or,  in  other 
words,  the  distance  a  a'  represents  the  total  electromotive 
force  of  the  battery.  If  the  circuit  is  opened  or  broken  be- 
tween L  and  E  so  that  no  current  flows,  then  the  difference 


Fig.  914. 

of  potential  between  the  conductor  and  the  earth  is  the 
same  at  all  points  along  the  conductor,  and  is  represented 
by  the  distances  between  the  line  C  D  and  the  conductor 
A  L. 

But  when  a  current  is  allowed  to  flow  along  the  conductor, 
the  difference  of  potential  between  the  conductor  and  the 
earth  decreases  in  tJie  direction  in  zvJiicJi  tJie  current  is  floiv- 
ing.  The  vertical  distances  b  b' ,  c  c\  d d\  etc.,  represent 
this  difference  of  potential  at  the  points  b,  c,  d,  etc.,  along 
the  conductor.  The  loss  or  drop  of  potential  is  represented 
by  the  vertical  distances  between  the  inclined  line  C  L  and 
the  horizontal  line  C  D.  This  loss  or  drop  also  represents 
the  difference  of  potential  between  the  point  a  and  any  other 
point  along  the  conductor.     For  example,  at  h  the  differ- 


ELECTRICITY  AND  MAGNETISM.  1497 

ence  of  potential  between  the  conductor  at  that  point  and 
the  earth  is  represented  by  the  distance  h  h' ;  the  loss  or 
drop  of  potential  is  represented  by  the  vertical  distance 
between  h'  and  the  horizontal  line  C  D,  which  distance  also 
represents  the  difference  of  potential  existing  between  the 
points  a  and  h. 

2315.     The  graphical  method  of  determining  the  dif- 

ference  of  potential  is  seldom  used.      Ohm's  latv  not  only 

gives  the  strength  of  the  current  in  a  closed  circuit,  but  also 

the  difference  of  potential  in  volts  along  that  circuit.     The 

difference  of  potential  (^')  in  volts  between  any  two  points 

along  a  circuit  is  equal  to  the  product  of  the  strength  of  the 

current  (C)  in  amperes  and  the  resistance  (7?')  in  ohms  of 

that  part  of  the  circuit  between  those  two  points  ;  or  ii '  = 

C R\  which  is  an  example  of  the  use  of  formula  411.     E' 

also  represents  the  loss  or  drop  of  potential  in  volts  between 

the  two  points.     If  any  two  of  these  quantities  are  known, 

E' 
the  third  can  be  readily  found  ;  for,  by  transposing,  C  =-™ 

K. 

E' 
and  R  =  -f^,  as  already  given  in  formulas  409  and  410. 

Example. — Fig.  915  represents  part  of  a  circuit  in  which  a  current 
of  2.5  amperes  is  flowing.    The  a  h  e  d 

resistance  from   a  to  (5  is  10  '  '         t 


ohms  ;   from  b  to  c,  15  ohms,  Fig-  915. 

and  from  c  to  d,  20  ohms.     Find  the  difference  of  potential  between 

a  and  b,  b  and  c,  c  and  d,  and  a  and  d. 

Solution. — Since,  by  formula  411,  -£"'  =  CT?',  then 
The  difference  of  potential  between 

a  and  (5  is  2.5  X  10  =  25  volts  ; 

b  and  c  is  2.5  X  15  =  37.5  volts  ; 

c  and  ^  is  2.5  X  20  =  50  volts  ; 

a  and  ^ is  25  +  37.5  +  50  =  112.5  volts; 
or,  in  other  words,  the  loss  or  drop  in  potential  between  a  and  d  is 
112.5  volts. 

2316.  In  a  great  many  cases,  it  is  desirable  to  have  the 
current  flow  from  the  source  a  long  distance  to  some  electric 
receptive  device,  and  return  without  causing  an  excessive 
drop  or  loss  of  potential  in  the  conductors  leading  to  and 


1498  PRINCIPLES  OF 

from  the  two  places.  In  such  circuits,  the  greater  part  of 
the  total  generated  electromotive  force  is  expended  in  th.e 
receptive  device  itself,  and  only  a  small  fraction  of  it  is  lost 
in  the  rest  of  the  circuit.  Under  these  conditions,  it  is  cus- 
tomary to  decide  upon  a  certain  drop  or  loss  of  potential 
beforehand,  and  from  that  and  the  current  calculate  the 
resistance  of  the  two  conductors. 

Example. — It  is  desired  to  transmit  a  current  of  10  amperes  to  an 
electrical  device  situated  1,000  feet  from  the  source ;  the  total  generated 
E.  M.  F.  is  110  volts,  and  only  5^  of  this  potential  is  to  be  lost  in  the 
conductors  leading  to  and  from  the  two  plants.  Find  (a)  the  total 
resistance  of  the  two  conductors,  and  (d)  the  resistance  per  foot  of  the 
conductors,  assuming  each  to  be  1,000  feet  long. 

Solution. —  5%  of  110  volts  =  110  X  -05  =  5.5  volts,  which  represents 
the  total  drop  or  loss  of  potential  on  the  two  conductors.  Let  ^'  =  5.5 
volts  ;  C=10  amperes,  and  i?'  =  the  total  resistance  of  the  two  con- 

ductors.     Then,  by  formula  410,  7?'  =-^  =  -^  =  .55  ohm.      (a)  Ans. 

The  resistance  per  foot  of  the  conductor  is  found  by  formula  406. 
In  this  case,   ri  =  .55  ohm  ;   A  =  3,000  feet  ;   4  =  1  foot.     Then,   the 

55  X  1 

resistance  per  foot  =  ra  =  'yqqo'  —  -000375  ohm.     (3)  Ans. 


EXAMPLES  FOR  PRACTICE. 

1.  In  a  part  of  a  closed  circuit,  the  drop  or  loss  of  potential  caused 
by  the  resistance  of  the  conductor  is  10  volts.  If  the  current  flowing 
is  4  amperes,  what  is  the  resistance  of  that  part  of  the  circuit  ? 

Ans.  3.5  ohms. 

3.  The  total  generated  electromotive  force  in  a  circuit  is  320  volts. 
A  current  of  10  amperes  is  transmitted  to  and  from  a  receptive  device 
situated  110  feet  from  the  source,  with  a  loss  of  potential  of  10^.  (a) 
Find  the  total  resistance  of  the  two  conductors  leading  to  and  from 
the  two  places,  and  {^)  find  the  resistance  per  foot  of  each  conductor, 
assuming  each  to  be  alike  and  110  feet  long. 

Ans  ^^^'^  3.2  ohms. 
.  '  (  (^)  .01  ohm  per  foot. 

TOTAL  AND  AVAILABLE  E.  M.  F. 

2317.  The  difference  of  potential  between  the  two 
electrodes  of  a  simple  voltaic  cell  when  no  current  is  flow- 
ing, that  is,  when  the  circuit  is  o/>en,  is  always  equal  to  the 
total   electromotive   force   developed   within   the   cell;  but 


ET.ECTRICITY  AND  MAGNETISM.  1499 

when  a  current  is  flowing,  that  is,  when  the  circuit  is  closed, 
a  certain  amount  of  potential  is  expended  in  forcing  the 
current  through  the  internal  resistance  of  the  cell  itself. 
Consequently,  the  difference  of  potential  between  the  two 
electrodes  when  the  circuit  is  closed  is  always  smaller  than 
when  the  circuit  is  open.  This  difference  of  potential  when 
the  circuit  is  closed  is  sometimes  called  the  available  or  ex- 
ternal electromotive  force,  to  distinguish  it  from  the  internal 
or  total  generated  electromotive  force. 

2318.  The  available  electromotive  force  is  equal  to  the 
difference  between  the  total  generated  electromotive  force 
and  the  potential  expended  in  forcing  the  current  through 
the  internal  resistance  when  the  circuit  is  closed.  From 
Ohm's  law,  this  loss  or  drop  of  potential  in  the  cell  itself  is 
equal  to  the  product  of  the  internal  resistance  and  the 
strength  of  current  flowing. 

Let  E  =  total  generated  E.  M.  F. ; 
E'  =  available  E.  M.  F. ; 

C  =  current  flowing  when  the  circuit  is  closed; 
r,-  =  internal  resistance  of  the  cell; 
re  =  an  external  resistance. 

The  drop  or  loss  of  potential  in  the  cell  =  Cr^  and  E'  = 
E-Cr,. 

2319.  For  example,  in  a  voltaic  cell  the  total  generated 

E.  M.  F.  is  2  volts,  and  the  internal  resistance  is  4  ohms. 

If  the  two  electrodes  are  connected  to  an  external  resistance 

of  6  ohms,  a  current  of  .2  ampere  will  flow  through   the 

E  2 

circuit,    since    C= ; =  - -=.2    ampere.       The   loss 

r,  +  r,      4+G 

or  drop  of  potential  in  the  cell  =  C r^  =  .2  X  4:  =  .S  volt. 
Then,  E'  =  E  —  C r^  =  2  —  .8  =  1.2  volts,  which  is  the  elec- 
tromotive force  available  to  force  the  current  of  .2  ampere 
through  the  external  resistance  of  6  ohms,  since  Crg=  .fix 
6=1.2  volts. 


1500  PRINCIPLES  OF 

OHM'S  LA^W  APPLIED    TO    DERIVED  CIRCUITS. 

2320.  A  derived  or  shunt  circuit  is  a  brancJi  or  additional 
circuit  provided  at  any  part  of  a  circuit  through  which  the 
current  branches  or  divides,  part  flowing  through  the  original 
circuit  and  part  through  the  new  branch. 

A  derived  circuit  is  in  multiple  circuit  with  the  circuit 
from  which  it  is  derived. 

In  the  case  of  branched  circuits,  each  of  the  branches  acts 
as  a  derived  circuit  to  the  others.  Any  number  of  additional 
branches  may  thus  be  provided. 

2321.  In  treating  upon  derived  or  shunt  circuits,  only 
that  part  of  the  circuit  will  be  considered  which  is  divided 
into  branches  and  each  branch  transmitting  part  of  the  cur- 
rent; the  rest  of  the  circuit  is  assumed  to  be  closed  through 
some  electric  source;  as,  for  instance,  a  voltaic  battery. 

Before  applying  Ohm's  law  to  derived  circuits,  it  is  nec- 
essary that  the  meaning  of  conductivity  should  be 
thoroughly  understood.  In  Art.  2217  it  was  stated  that 
conductivity  is  the  inverse  of  resistance ;  or,  in  other  words, 
it  is  the  reciprocal  of  resistance. 

Therefore,  since  the  conductivity  is  greater  the  less  the 
resistance,  the  conductivity  may  be  defined  as  being  equal 

to  -^;  that  is,  the  reciprocal  of  the  resistance. 

2322.  The  conductivity  of  any  conductor  is,  therefore, 
unity  divided  by  the  resistance  of  the  conductor;  and,  con- 
versely, the  resistance  of  any  conductor  is  unity  divided  by 
the  conductivity  of  that  conductor.  For  example,  if  the 
resistance  of  a  circuit  is  2  ohms,  the  conductivity  is  repre- 
sented by  -75-  =  -I ;  if  the  resistance  is  increased  to  4  ohms, 

the  conductivity  would  be  only  one-half  as  much  as  in  the 
first  case,  and  would  now  be  \. 

There  is  no  established  unit  of  conductivity;  it  is  used 
merely  as  a  convenience  in  calculation. 

2323.  Fig.  916  represents  a  derived  circuit  of  two 
branches. 


ELECTRICITY  AND  MAGNETISM.  1501 

Let  r^  and  i\  =  the  separate  resistances  of  the  branches, 
respectively; 
C^  and  c^  =  the  currents  in  each  branch,  respectively ; 
C  =  the  current  in  the  main  circuit. 

Then,  r,  4^  c^  =  C. 

When  the  current  flows  from  a  to  b,  if  the  resistances  r, 
and  r^  are  equal,  the  current  will  divide  equally  between 
the  two    branches.      Thus,  ^ 

if  a  current   of   2  amperes  C  ^     ^^    ^ 

is  flowing  in  the  main  cir-  \^       y^ 

cuit,    1    ampere    will    flow  c^  * 

through  each  branch.  ^^°-  ^^^• 

When  the  resistances  are  unequal,  the  current  will  divide 
inversely  as  the  respective  resistances  of  the  two  branches; 
or,  since  the  conductivity  is  the  reciprocal  of  the  resistance, 
the  current  zvill  divide  in  proportion  to  their  respective  con- 
ductivities. 

In    Fig.  916  the  conductivities  of  the  two  branches   are 

—  and  — ,  respectively. 

Therefore,  2      2  c       r 

c  '  c   •  •  —  *  —     or  —  =  — . 

Example. — Given  C  =  60  amperes  ;  r,  =  3  ohms  ;  ra  =  3  ohms. 
Find  Ci  and  fa- 

Solution. —    —  =  — ,  or  ~  z=—,   or  ^,  =  -^.     But  r,  +  <ra  =  60,  or 

3  Co 
f,  =  60  — (Ta.      Substituting   for   the   value   of   c-^    gives   60  — <:i  =  -^. 

Transposing  gives  5  ^a  =  120,  or  d  =  24  amperes.  Ans.     ^1  =  60  --  24  — 
36  amperes.  Ans. 

23Z4:.  It  is  clear  that  two  conductors  in  parallel  will 
conduct  an  electric  current  more  readily  than  one  alone; 
that  is,  their  joint  conductivity  is  greater  than  either  of 
their  separate  conductivities  taken  alone.  This  being  the 
case,  their  resistances  must  follow  the  inverse  law;  viz., 
the  joint  resistance  of  two  conductors  in  parallel  must  be 
less  than  either  of  their  separate  resistances  taken  alone 
Hence- 


1503  PRINCIPLES  OP 

Rule. — If  the  separate  resistances  of  two  conductors  are 
equal,  their  Joitit  resistance  when  connected  in  parallel  is  one- 
half  of  their  separate  resistance. 

2325.  When  the  separate  resistances  of  two  conductors 
in  parallel  are  unequal,  the  determination  of  their  joint 
resistance  when  connected  in  parallel  involves  some  calcu- 
lation. 

In  Fig,  916  the  conductivities  of  the  branches  are  —  and  — , 

1  a 

respectively. 

1        1        r  ■\-r 
Their  joint  conductivity  = Ht  ~  ~ ''■> 

' 1         '  »  \ 'a 

their  joint  resistance  72"  =  1  -^  !l±Ii  =     ^^,^^  .  (41 2.) 

12  2  "T"    '  J 

Rule. —  The  joint  resistance  of  tivo  conductors  in  parallel 
is  equal  to  the  product  of  their  separate  resistances  divided  by 
the  sum  of  their  separate  resistances. 

Example. — In  Fig.  916,  given  ri  =  4  ohms  ;  ra  =  6  ohms,  and  C=  30 
amperes.  Find  Cx  and  ^2  in  the  separate  branches  and  the  joint  resist- 
ance of  the  branches  from  atob. 

Solution. —    —  =  — ,  or  Cx  =  — r^-     But  ^1  +  ^2  =  30,  or  ^  1  =  30  —  (Tj  ; 
^2      4  4 

6  c 
substituting,    30  —  ^2  =  —~^.     Reducing    gives  10  c^  =  120,   or  c^  =  13 

amperes.     Ans.     ^Ti  =  30  —  12  =  18  amperes.     Ans. 

jr  ;-„       4  X  6 
By  formula  412,  the  joint  resistance  R"  =  - =-  =— -—  =  2.4  ohms. 

■^  '         -^  ;'2  +  Tx        10 

Ans 

2326.  Fig-  917  represents  a  derived  circuit  of  3  branches. 
JXy — ^^  Let  Tj,  r^,  and  r^  =  the  sepa- 

C  ^     „{        rf  \h     *-    X2^.Q.  resistances  of  the  three 

branches,  respectively ;  then, 

ci^  —  ,    — .    and  —  represent  the 

Fig.  917.  ^j      ^2  ^3 

separate  conductivities  of  the  three  branches,  respectively. 

1        1        1        rr-\-rr-\-rr 
Their  joint  conductivity  =-—  +  -+---.    '   "        '    ' '—- 

'  \  '  1  '  %  123 

Since   the   joint  resistance   is  the   reciprocal   of   the  joint 
conductivity,  then 


ELECTRICITY  AND  MAGNETISM.  1503 

the  joint  resistance  of  the  three  branches  in  parallel  from 
a  to  d.     We  have,  therefore,  the  following 

Rule. —  The  joint  resistance  of  three  or  more  conductors  in 
parallel  is  equal  to  the  reciprocal  of  their  joint  conductivity. 

Example. — In  Fig.  917,  given  r^,  =  5  ohms,  r^  =  10  ohms,  and  ra  =  20 

ohms.     Find  their  joint  resistance  from  a  to  ^. 

Solution. — By  formula  413  the  joint  resistance 

„,„  _  r,  r,  ra  ^ 5  X  10  X  20 ^  1,000  _ 

""  ra  rs  +  ri  rs  +  r,  r^       (10  X  20)  +  (5  X  30)  +  (5  X  10)        350  ~ 

20 

—  =  2f  ohms.     Ans. 

2>32'7,  In  any  derived  circuit,  the  difference  of  po- 
tential between  where  the  branches  divide  and  where  they 
unite  is  equal  to  the  product  of  the  sum  of  the  currents  in 
the  separate  branches  and  their  joint  resistance  in  parallel, 
as  will  be  apparent  from  consideration  of  Ohm's  law,  Art. 
231 0.  For  example,  if  the  currents  in  the  three  branches, 
Fig.  917,  are  16,  8,  and  4  amperes,  respectively,  and  the 
joint  resistance  from  a  to  I;  is  2-|  ohms,  then  the  difference 
of  potential  between  a  and  d  is  (16  +  8  +  4)  X  2f  =  28  X 
^0.  —  80  volts. 

2328.  The  separate  currents  in  thie  branches  of 

a  derived  circuit  can  be  determined  by  finding  the  difference 
of  potential  between  where  the  branches  divide  and  where 
they  unite,  and  dividing  the  result  by  the  separate  resist- 
ance of  each  branch.  For  example,  in  Fig.  917  assume 
that  the  difference  of  potential  between  a  and  d  is  80  volts, 
and  that  the  separate  resistances  of  the  three  branches  are, 
respectively,  5,  10,  and  20  ohms.  Then  the  current  in  the 
first  branch  is  -V- =  16  amperes;  in  the  second,  -1-^=8  am- 
peres, and  in  the  third,  |-2-  =  4  amperes. 

2329.  The  separate  resistances  of  the  branches 

of  a  derived  circuit  can  be  determined  by  finding  the  dif- 
terence  of  potential  between  where  the  branches  divide  and 


1504  PRINCIPLES  OF 

where  they  unite,  and  dividing  the  result  by  the  separate 
currents  in  each  branch.  For  example,  in  Fig.  917  assume 
the  difference  of  potential  between  a  and  b  to  be  80  volts, 
and  the  currents  in  the  separate  branches  to  be  16,  8,  and  4 
amperes,  .respectively;  then,  the  resistance  of  the  first 
branch  is  -f-^-  =  5  ohms;  of  the  second,  -§§3-  =  10  ohms,  and  of 
the  third,  ^-^  —  20  ohms. 

EXAMPLES  FOR  PRACTICE. 

1.  The  separate  resistances  of  two  branches  X  and  F  of  a  derived 
circuit  are  13  and  29  ohms,  respectively.  Find  their  joint  resistance  in 
parallel.  Ans.  8.9762  ohms. 

2.  The  sum  of  the  currents  in  two  branches  X  and  F  of  a  derived 
circuit  is  28  amperes.  If  the  separate  resistance  of  X  is  7  ohms  and 
the  separate  resistance  of  F  is  4  ohms,  what  is  the  separate  current  in 
each  branch  ?  a        i  Current  in  branch  ^is  10.1818  amperes. 


Ans. 


Current  in  branch  Fis  17.8182  amperes. 

3.  The  separate  resistances  of  three  branches  of  a  derived  circuit 
are,  respectively,  36,  45,  and  64  ohms.  Find  their  joint  resistance  in 
parallel.  Ans.  15.2381  ohms. 

4.  The  joint  resistances  of  three  conductors  X,  F,  and  Z,  connected 
in  parallel,  is  2.5  ohms.  If  the  separate  currents  in  the  branches  are, 
respectively,  .6,  .7,  and  .8  ampere,  what  is  the  separate  resistance  of 
each  branch  ?  /  Resistance  of  branch  X=  8.75  ohms. 

Ans.  "I  Resistance  of  branch  F=  7.5  ohms. 

'  Resistance  of  branch  Z  =■  6.5625  ohms. 

5.  The  separate  resistances  of  three  branches  X,  V,  and  Z  of  a  de- 
rived circuit  are  2,  3,  and  4  ohms.  If  the  sum  of  the  currents  in  the 
three  branches  is  26  amperes,  what  is  the  separate  current  in  each 
branch  ?  T  12  amperes  in  branch  X. 

Ans.  "j    8  amperes  in  branch  F. 
'    6  amperes  in  branch  Z. 

THE  JOULE. 

2330.  The  practical  unit  of  electric  energy  or  work  is 
the  Joule. 

The  joule  is  greater  than  the  absolute  unit  of  energy  or 
work,  the  erg  (Arts.  2263  and  2264). 

1  absolute  unit  or  erg  equals  one-ten-millionth  (  TTrT^T^Trr;?^  I 

part  of  a  joule. 

One  joule  equals  ten  million  (10,000,000)  absolute  units 
or  ergs. 


ELECTRICITY  AND  MAGNETISM.  1505 

ELECTRICAL,  •WORK. 

2331.  The  joule  may  be  further  defined  as  being  that 
amount  of  energy  zvhicJi  is  expended  diiring  the  time  of  one 
second^  by  one  ampere  in  overcoming  the  resistance  of  one  ohm. 

2332.  But  1  ampere  flowing  for  1  second  =  1  coulomb 
(Art.  2280) ;  and  1  ampere  flowing  through  1  ohm  = 
1  volt  ^Art.  2304) ;  therefore,  1  joule  may  be  defined  as 
being  that  amount  of  energy  expended  when  1  volt  propels  1 
coulomb,  or  when  1  coulomb  is  carried  through  a  distance 
between  which  the  difference  of  potential  is  1  volt. 

The  work  done,  therefore,  may  be  said  to  be  one  volt- 
coulomb,  just  as  in  mechanics  the  work  done  by  raising 
1  pound  through  1  foot  is  equal  to  the  foot-pound. 

2333.  This  volt-coulonib,  however,  which  is  called 
the  joule,  is  not  as  great  as  the  foot-pound,  the  relation  being 

1  joule  =  .7373  foot-pound. 

1  foot-pound  =  1.356  joules. 
We  may  now  state  the  rule  for  the  determination  of  elec- 
trical work  as  follows: 

2334.  Rule. —  To  find  the  amount  of  electrical  work 
accomplished  in  joules  during  a  given  time^  multiply  the  quan- 
tity of  electricity  in  coulombs  tvJiich  has  passed  in  the  circuit 
during  that  time  by  the  loss  or  drop  of  potential. 

2335.  This  rule  may  be  expressed  by  the  following 
formulas,  for  the  three  cases  occurring  in  practical  work: 

Let  J  =  electrical  work  in  joules; 
C  =  current  in  amperes ; 

t  =  time  in  seconds  during  which  current  flows; 
E=  E.  M.  F.  of  circuit; 
R  =  resistance  of  circuit. 
Then,  according  to  Art.  2334, 

y=  coulombs  X  drop. 

But,  according  to  Art.  2280,  ampere-seconds  =  cou- 
lombs ;  so  that 

j  =  amperes  X  seconds  X  drop. 


J 506  PRINCIPLES  OF 

But,  according  to  Art.  231 6,  drop  =  current  X  resist- 
ance; hence, 

J  =  amperes  x  seconds  X  amperes  X  resistance, 
which  can  be  written,  by  utihzing  the  notation  given  above,  as 

/=  CY,txCY.R', 
or,  J=ORt.         (414.) 

This  formula,  then,  gives  the  electrical  work  in  joules 
when  the  current  and  resistance  are  known. 

Example. — Find  the  amount  of  work  done  in  joules  when  a  current 
of  15  amperes  flows  for  \  hour  against  a  resistance  of  2  ohms. 

Solution. —  ^  hour  =  1,800  seconds.  By  formula  4 14,  the  electrical 
work  done 

/  =  C2i?/  =  15xl5x3X  1,800  =  810,000  joules.     Ans. 

2336.  When  the  current  and  electromotive  force  are 
known,  we  derive  the  formula  for  the  electrical  work  as 
follows: 

According  to  Art.  2334, 

/=  coulombs  X  drop. 
But  drop  =  E  and  coulombs   (as   in  Art.   2335)   equal 
C  t\  hence, 

J^CEt.         (415.) 

This  formula  expresses  the  amount  of  the  electrical  work 
in  terms  of  current  and  drop. 

Example. — Find  the  amount  of  work  in  joules  done  in  1  hour  by 
a  current  of  25  amperes  under  an  electromotive  force  of  20  volts. 

Solution. —  1  hour  =  3,600  seconds.  By  formula  41 5,  the  electrical 
work 

/=  CEt~  25  X  20  X  3.600  =  1,800,000  joules.     Ans. 

2337.  When  the  electromotive  force  and  resistance  only 
are  known,  we  proceed  in  a  similar  manner. 

Again,  according  to  Art.  2334, 

y  =  coulombs  X  drop. 
But  coulombs  (Art.  2335)  =  C  t  and  drop  =  E\  hence. 

J=CtE, 


ELECTRICITY  AND  MAGNETISM.  1507 

But,  according  to  Ohm's  law  (Art.  231 0,  formula  409), 

E  .  . 

C=^-r,,  and  inserting  this  value  of  C,  we  have 

XV. 

or,  ■^=nr-      ('''^®-' 

This  formula  expresses  the  amount  of  the  electrical  work 
in  terms  of  the  E.  M.  F.  and  resistance. 

Example. — What  is  the  amount  of  work  done  in  joules  in  45  min- 
utes in  a  circuit  having  200  ohms  resistance,  the  electromotive  force 
being  110  volts  ? 

Solution. —  45  minutes  =  2,700  seconds.  By  formula  416,  the 
electrical  work  done 

^     £'/      110X110X2,700      ,.„„.^.     ,  . 

/=  —r=-  =  • jr— r =  163,350  loulcs.     Ans. 

•^  K  200 

2338.  As  stated  in  Art.  2333,  the  joule  =  .7373  foot- 
pound; therefore,  when  the  work  in  joules  is  known,  the 
work  in  foot-pounds  is 

F.  P.  =.7373/,         (417.) 
which  may  be  expressed  by  the 

Rule. —  T/ie  eqiiivalent  zvork  do7te  in  foot-pounds,  when 
the  work  in  joules  is  known,  is  obtained  by  -multiplying  the 
number  of  joules  by  .  7373. 

Example. — Express  the  work  accomplished  in  foot-pounds  in  a 
circuit  where  a  current  of  8  amperes  flows  for  2  hours,  the  electro- 
motive force  being  10  volts. 

Solution. —  2  hours  =  7,200  seconds  = /.  By  formula  415,  the 
electrical  work  done  =/=  8  X  10  X  7,200  =  576,000  joules.  Expressed 
in  foot-pounds,  this  will  be  by  formula  417, 

F.  P.  =  .7373  X  576,000  =  424,684.8  foot-pounds.  Ans. 

Example. — Find  the  amount  of  work  done  in  foot-pounds  by  a  cur- 
rent of  4  amperes  flowing  for  15  seconds  against  a  resistance  of  3  ohms. 

Solution. — By  formula  414,  the  electrical  work  done  =  /=:4x 
4  X  3  X  15  =  720  joules.  The  mechanical  work  done,  by  formula  417, 
in  foot-pounds  is  F.  P=  =  .7373  X  720  =  530.856  foot-pounds.     AnSc 


1508  PRINCIPLES  OF 

RELATIONS    OF    MECHANICAL,    ELECTRICAL,    AND     HEAT 

ENERGY- 

2339.  When  an  electric  current  flows  from  a  higher  to 
a  lower  potential,  electrical  energy  is  expended  and  work 
is  done. 

This  energy  is  expended  in  overcoming  the  resistance  of 
the  conductor  constituting  the  circuit. 

In  the  case  of  analogy  IV.,  Art.  2313,  the  friction  of 
the  water  against  the  walls  of  the  pipe  produces  heat,  in  an 
exactly  similar  manner  as  heat  is  produced,  for  instance,  by 
rubbing  sandpaper  over  a  wooden  surface.  In  the  latter 
case,  however,  the  friction  is  very  great,  and  the  heat  pro- 
duced is  hence  quickly  felt  by  the  hand,  while,  in  the  case  of 
water  against  metal  pipes,  the  friction  is  comparatively  very 
small,  and  the  heat  produced  thereby  is  not  perceptible  to 
our  sense  of  touch.  Nevertheless,  the  heat  is  there,  as  the 
principle  of  the  conservation  of  energy  proves  (see  Art. 
960).  This  heat  is  dissipated  into  the  surrounding  atmos- 
phere; it  is,  therefore,  not  destroyed,  but  merely  exists  in 
another  form,  having  gone  to  increase  the  temperature  of 
the  air. 

3340.  Exactly  so  is  it  with  the  energy  expended  by  an 
electric  current  in  overcoming  the  resistance  of  a  con- 
ductor ;  that  is  to  say,  when  a  quantity  of  electricity  flows 
against  the  resistance  of  a  conductor,  a  certain  amount  of 
electrical  energy  is  transformed  into  lieat  energy.  This 
fact  becomes  very  noticeable  at  times,  for  the  conductor  may 
become  exceedingly  hot — so  hot,  indeed,  that  unless  due 
care  is  exercised  the  wire  carrying  the  current  may  be 
melted  by  the  great  heat  produced. 

2341.  The  actual  amount  of  heat  developed  is  an 
exact  equivalent  of  the  work  done  in  overcoming  the  resist- 
ance of  the  conductor,  and  varies  directly  as  that  resistance. 
For  example,  take  two  wires,  the  resistance  of  one  being 
twice  that  of  the  other,  and  send  currents  of  equal 
strengths  through  each.  The  amount  of  heat  developed  in 
the  wire  of  higher  resistance  will  be  twice  that  developed  in 


ELECTRICITY  AND  MAGNETISM.  1509 

the  wire  offering  the  lower  resistance.  The  distinguished 
scientist  y(9?/;/r,  after  whom  the  practical  unit  of  energy  is 
named,  made  elaborate  experiments  to  determine  exactly 
what  relation  existed  between  the  mechanical  or  electrical 
work  done  and  the  heat  thereby  generated. 

2342.  Mechanical  Equivalent  of  Heat. — Joule 
found,  as  shown  in  Art.  1148,  that  the  heat  which  is  gen- 
erated by  doing  778  foot-pounds  of  work  is  exactly  equal  to 
the  amount  of  heat  required  to  raise  the  temperature  of  1 
pound  of  pure  water  1°  F.,  at  or  near  39°  F.,  the  tempera- 
ture of  its  maximum  density.  This  amount  of  heat  is  called 
one  British  Thermal  Unit  (written  B.  T.  U.). 

Therefore,  we  have  the  relation 

778  foot-pounds  =  1  B.  T.  U. 

1  foot-pound    =  .001285  B.  T.  U. 
This  relation  is  called  the  mechanical  equivalent  of 
heat. 

2343.  Electrical  Equivalent  of  Heat;  Joule's 
Law. — Upon  investigating  the  amount  of  heat  generated 
by  an  electrical  current  when  overcoming  the  resistance  of 
a  conductor.  Joule  found  that  one  ampere  of  current  flowing 
through  one  ohm  of  resistance  during  the  time  of  one  second 
always  developed  .0009477  British  Thermal  Unit. 

He  found  furthermore  that  the  development  of  heat  was 
proportional, 

1.   To  the  resistance  of  the  conductor  ; 
3.   To  the  square  of  the  current  strength  ; 
3,    To  the  time  during  which  the  current  flows  ; 
so  that  if 

//"==  B.  T.  U.  developed  in  the  circuit  ; 
C  =  current  in  amperes  ; 
R  =  resistance  in  ohms  ; 
/  =  time  in  seconds, 
then  the  general  formula  for  the  development  of  heat  in  any 
electrical  circuit  is  given  by  what  is  called  Joule's  La^v,. 

^=.0009477  (T'ie/.  (418.) 


1510  PRINCIPLES  OF 

Example. — Determine  how  many  B.  T.  XJ.  are  developed  in  an  elec- 
trical circuit  having  a  resistance  of  180  ohms,  through  which  a  current 
of  2  amperes  flows  for  1  minute. 

Solution. —  /  =  60  seconds  ;  C=2  ;  7?  =  180  ;  hence,  by  formula 
418,  the  heat  units  developed  are 

11=  .0009477  X  2  X  3  X  180  X  60  :=  40.94  B.  T.  U.     Ans. 

2344.  Referring  back  to  Art.  2335,  we  find  that  the 
work  in  joules  performed  in  an  electrical  circuit  is  given  by 
a  formula  similar  to  formula  418  ;  in  fact,  we  find  that  the 
work  in  joules  is  proportional  to  the  same  factors  as  the 
heat  development.  This  relation  is  best  made  clear  by  solv- 
ing the  following 

Example. — Given  an  electrical  circuit  having  a  resistance  of  2  ohms, 
in  which  a  current  of  2  amperes  flows  for  2  seconds,  determine  (a)  the 
work  in  joules  done  in  this  circuit,  and  (d)  the  number  of  B.  T.  U. 
developed  in  the  circuit. 

Solution. —  /  =  3;  C=2  ;  R  =  2  ;  then,  by  formula  414,  the  work 
in  joules,  («:)/=  C2  7?/  =  3x  2x2x  2  =  16  joules.  Ans.  And  by  for- 
mula 41 8,  {b)  ^=.0009477  C^  R  t  =  .0009477  x2x2x3X2  =.0151632 
B.  T.  U.     Ans. 

2345.  We  therefore  see  that  the  circuit  of  the  prece- 
ding example  develops  .0151033  heat-unit  when  16  joules  of 
work  are  done. 

Consequently,  we  have  the  relation 

16  joules  =  .0151632  B.  T.  U.  •, 
or,  1  joule  =  .0009477  B.  T.  U. ; 

and,  conversely,  1  B.T.U.=  1,055.20  joules. 

Now,  since  we  know  that  .7373  foot-pound  of  mechanical 
work  is  equivalent  to  1  joule  of  electrical,  and  since  1  joule 
of  electrical  work  equals  .0009477  heat-unit,  it  is  clear  that 
we  have  established  a  complete  relation  between  me-chanical 
work,  electrical  work,  and  heat  energy,  so  that  any  one  of 
these  three  energies  can  be  mathematically  expressed  in 
terms  of  the  others.  These  relations  are  expressed  clearly 
by  Table  78. 

2346.  The  following  table  will  be  found  very  useful  for 
all  examples  involving  transformations  of  energy  : 


ELECTRICITY   AND    MAGNETISM.  1511 

TABLE  78. 

ENERGY   EQUIVALENTS. 

Heat  Energy.  Mechanical  Energy.  Electrical  Energy. 

1.000000    B.T.U.  =  778.0000 foot-pounds  =  1,055.2000 joules. 
.001285    B.T.U.=      1.0000  foot-pound    =  1.3563  joules. 

. 0009477  B.T.U.=        .7373  foot-pound    =  1.0000  joule. 

Example. — Given  an  electrical  circuit  having  a  resistance  of  3  ohms, 
through  which  a  current  of  5  amperes  flows  for  1  hour,  determine 
(a)  the  work  done  in  joules;  (d)  how  many  foot-pounds  this  work  is 
equivalent  to;  (c)  the  number  of  heat-units  developed. 

Solution. —  /  =  3,600  seconds;  C=  5  amperes;  7?  =  3  ohms;  then, 
by  formula  414,  the  work  in  joules 

(rt)  /=  C^  7?  /  =  5  X  5  X  3  X  3,600  =  270,000  joules.     Ans. 

According  to  Table  78,  1  joule  =  .7373  foot-pound;  hence, 

{d)  270,000  X  .7373  =  199,071  foot-pounds.     Ans. 

According  to  Table  78,  1  foot-pound  is  equivalent  to  a  heat  develop- 
ment of  .001285  B.  T.  U. ;  hence, 

{c)  199,071  X  .001285  =  255.81  B.  T.  U.     Ans. 


ELECTRICAL  POUVER. 

2347.  The  total  amount  of  work  done  is  independent 
of  time  (see  Art.  954) ;  that  is  to  say,  the  total  work  is  the 
same  whether  it  is  done  in  one  minute  or  in  one  year.  But 
when  various  amounts  of  work,  done  in  different  times,  are 
to  be  compared  to  a  common  standard  of  power,  the  element 
of  time  must  be  considered. 

Similarly  in  the  electrical  circuit;  the  total  number  of 
joules  of  work  done  is  independent  of  the  time,  but  when 
there  are  several  circuits,  the  work  of  each  of  which  is  to 
be  compared  to  a  standard,  the  element  of  time  in  which 
this  work  is  done  must  be  considered. 

2348.  In  practical  mectianical  work  the  unit  of 
time  is  always  one  minute,  and  the  unit  which  measures  the 
work  performed  in  a  given  time  is  the   foot-pound  per 


1512  PRINCIPLES  OF 

minute.     This  unit   is  called   the   unit  of  mechanical 
power. 

Power  is,  therefore,  rate  of  doing  work,  and  hence  the 
power  exerted  can  always  be  determined  by  dividing  the 
work  done  in  foot-pounds  by  the  time  in  minutes  required 
to  do  it. 

2349.  In  practical  electrical  work  the  unit  of 
time  is  the  second,  and  the  unit  which  measures  the  work 
performed  in  a  given  time  is  the  joule  per  second.  This 
unit  is  called  the  unit  of  electrical  po^ver,  and  has  been 
named  the  watt. 

Hence,  if  in  a  certain  electrical  circuit,  say  1,000  joules 
of  work  are  done  in  10  seconds,  the  power  exerted  is 
1,000  -H  10  =  100  joules  per  second,  or  100  watts.  If  in 
another  circuit  the  same  work  is  done  in  5  seconds,  the 
power  there  exerted  is  1,000  -4-  5  =  200  joules  per  second, 
or  200  watts — just  twice  as  much.  Hence,  we  say  that  the 
power  exerted  in  the  second  circuit  is  twice  that  exerted  in 
the  first  ;  and  we  understand  thereby  that  if  in  both  circuits 
work  is  done  for  the  same  length  of  time,  the  second  circuit 
will  do  twice  as  much  work  as  the  first. 

3350.    Equation  of  Power  for  Electrical  Circuit. — 

The  equation  or  formula  expressing  the  power  exerted  in 
any  electrical  circuit  is  determined  as  follows  : 

According  to  Art.   2349,  electrical  power  is  expressed 
by  watts  =  joules  per  second. 
But,  according  to  Art.  2333, 

joules  =  volt-coulombs,  and  hence 
joules  per  second  =  volt-coulombs  per  second. 
Therefore,  also, 

watts  =  volt-coulombs  per  second. 
Now,  according  to  Art.  2280, 

coulombs  per  second  =  amperes. 
Inserting  this  value  in  the  next  before  the  last  equatJOn 
above,  we  have,  finally, 

watts  =  volts  X  amperes  % 


ELECTRICITY  AND  MAGNETISM.  1513 

or,  if  W=  total  watts  exerted  in  the  circuit  ; 

£  =z  volts  of  electromotive  force  ; 

C  =  current  in  amperes, 
then,  IV=£C,  (419.) 

which  may  be  expressed  by  the  following 

2351.  Rule. — hi  every  electrical  circuit  the  -poiver  in 
watts  is  equal  to  the  product  obtained  by  multiplying  the  cur- 
rent in  amperes  by  the  electromotive  force  in  volts. 

Example. — What  is  the  power  in  watts  in  an  electrical  circuit  in 
which  .6  ampere  flows  under  a  pressure  of  110  volts  ? 

Solution. —     C=.6  ;  E=  110  ;  hence,  by  formula  419, 
W—  ^  C  =  .6  X  110  =  66  watts.     Ans. 

2352.  When  \}vl^  power  is  to  be  expressed  by  the  cur- 
rent and  resistance.,  the  formula  is  obtained  as  follows  : 
According  to  formula  419,  we  have  W  ■=  E  C,  and  accord- 
ing to  formula  411,^=  C  R  ;  substituting  this  value  of 
E  =^  C  R'ln  formula  419,  we  have 

W=CxCxR=C'R,  (420.) 

which  may  be  expressed  by  the  following 

Rule. — In  every  electrical  circuit  the  power  in  watts  is 
equal  to  the  prodiLct  obtained  by  multiplying  the  square  of  the 
current  strength  in  amperes  by  the  resistance  of  the  circuit  in 
ohms. 

Example. — Determine  the  power  expended  in  watts  in  an  electrical 
circuit  having  a  resistance  of  183.3  ohms,  through  which  a  current  of 
.6  ampere  is  flowing. 

Solution. —  C=.6  ampere  ;  R  =  18B.%  ohms  ;  hence,  by  formula 
420,  fF=  C'^i?  =  . 6  X. 6x183.3  =  65.99  watts.     Ans. 

Note.— It  will  be  observed  that  this  result  is  the  same,  within  decimal 
limits,  as  that  obtained  from  the  example  in  Art.  ;2351.  It  is,  in  fact, 
the  same  circuit. 

2353.  When  the  power  is  to  be  expressed  by  the  electro- 
motive force  and  resistance,  the  formula  is  obtained  as 
follows:     According  to  formula  419,   we  have    W=EC, 

E 
and,  according  to  formula  409,  C=  -^;  substituting  this 


1514  PRINCIPLES  OF 

E 
value  of  (7=  -^  in  formula  419,  we  have 

W=^E  =  ^,  (421.) 

which  may  be  expressed  by  the  following 

Rule. — In  every  electrical  circuit  the  power  in  watts  is 
equal  to  the  quotient  obtained  by  dividing  the  square  of  the 
electromotive  force  in  volts  by  the  resistance  in  ohms. 

Example. — Determine  the  power  in  watts  of  an  electrical  circuit 
having  a  resistance  of  183.3  ohms  and  an  electromotive  force  of  110 
volts. 

Solution. —  .£"=110  volts;  i?  =  183.3  ohms;  hence,  by  formula 
421, 

,,.        E^         110  X  110        ac^c         ..  A 

W=-j^—  — ^p^  „    ■  =  66.0  watts.     Ans. 
K  loo.  o 

Note. — Observe  that  this  is  again  exactly  the  same  as  the  results 
obtained  from  the  examples  in  Arts.  2351  and  2352.  It  is,  in  fact, 
the  same  example  in  all  three  cases. 


ELECTRICAL   HORSEPOIVER. 

2354.  In  mechanical  calculations  the  foot-pound  per 

minute  is  found  too  small  a  unit  for  practical  use  ;  there- 
fore a  unit  has  been  adopted  having  the  value  of  33,000 
foot-pounds  per  minute,  which  is  about  equivalent  to  the 
power  a  strong  horse  can  exert.  This  unit  is,  therefore, 
named  the  liorsepo^ver.     (See  Art.  955.) 

2355.  Similarly  in  electrical  calculations  the  Joule  per 
second,  that  is,  the  -watt,  is  found  too  small  a  unit  for 
practical  use  ;  therefore  a  unit  has  been  adopted  having  a 
value  exactly  equivalent  to  the  value  of  the  mechanical 
horsepower.  This  unit  is  obtained  by  transforming  1  horse- 
power into  watts  as  follows  : 

1  mechanical  horsepower  =  33,000  foot-pounds  per  minute. 

33  000 
But  33,000  foot-pounds  per  minute  =  — '—- —  =  550  foot-pounds 

per  second.      Hence,    1  horsepower  =  550  foot-pounds  per 

second,  or  1  foot-pound  per  second  = :zirR .     And, 

ooO 


ELECTRICITY  AND  MAGNETISM.  1515 

according  to  Table  78,   1  joule  ==.7373  foot-pound;  hence, 
1  joule  per  second  or  1  watt  =  .7373  foot-pound  per  second, 

and,  hence,  1  foot-pound  per  second  =    ^^      . 

We  have,  therefore,  found  the  value  of  the  foot-pound  per 
second  expressed  both  in  horsepower  and  in  watts  ;  so  that 

-  ,  ,1  horsepower       1  watt 

1  foot-pound  per  second  = —^ =  , 

ooO  •to  Jo 

from  which  we  find  the  value  of 

550 
1  mechanical  horsepower  —  watts  =  746  watts.      (422») 

,  i  o  i  o 

This  value,  746  watts,  is  termed  one  electrical  horse- 
power. 

2356.  The  power  exerted  in  any  electrical  circuit  may 
now  be  expressed  in  horsepower  units  by  the  following 

Rule. —  To  express  the  rate  of  doing  electrical  work  in 
horsepower  units,  find  the  number  of  watts  and  divide  the 
result  by  7Jf6. 

If  H.  P.  =  horsepower; 
rF=  watts, 

W 
H.P.=^.  (423.) 

Since  W  has  the  various  values  given  by  formulas  419, 
420,  and  421,  the  horsepower  may  also  be  expressed  by 
three  other  equations: 

H.P.=^.  (424.) 

H,.P.  =^.  (425.) 

^•^•  =  7^-  (426.) 

2357.  "Before  giving  examples  on  the  application  of  the 
foregoing  formulas,  it  must  be  mentioned  that  a  practical 


1516  PRINCIPLES  OP 

unit  of  electrical  power  in  extended  use  is  the  kilowatt, 
having  the  value  of  1000  watts.  This  unit  is  usually  written 
K.  W.,  and  is  related  to  the  electrical  horsepower  by  the 
following  equations: 

1  K.  W.  =  1,000  watts  =  1.34  H.  P. 

1  H.   P.  =     746  watts  =    .746  K.  W. 

Example. — The  common  incandescent  electric  light  consists  of  a 
glass  bulb  containing  a  simple  carbon  conductor,  the  two  free  ends  of 
which  are  connected  to  the  source  of  the  electric  current.  When  the 
current  flows  through  this  conductor,  it  heats  it  to  such  a  degree  that 
it  becomes  white  hot,  or,  as  such  a  state  is  called,  incandescent.  If 
this  conductor  has  a  resistance  of  189.06  ohms  and  the  lamp  is  supplied 
with  an  electromotive  force  of  110  volts,  determine  the  following 
points  of  interest :  (a)  What  current  does  the  lamp  take  ?  (d)  How 
many  watts  does  it  consume  ?  (r)  How  many  B.  T.  U.  are  developed 
per  second  ?  (d)  How  many  such  lamps  would  one  electrical  horse- 
power keep  burning  ?  (e)  What  is  the  mechanical  equivalent  of  the 
heat  developed  per  second  in  the  lamp?  (/)  For  how  many  such 
lamps  would  10  K.W.  suffice? 

Note. — Regard  the  lamp  as  a  simple  conductor  of  the  stated  resist- 
ance in  solving  all  problems  relating  to  it. 

Solution.— (a)  ^=  110  ;  i?  =  189.06  ;  hence,  by  formula  409,  C  = 
E        110  .oo  A 

:^  =  189:06  =  --^^'^"^p^^"-  ^^'• 

((5)  By  solution  (rt),  C=. 582;  ^=110;  hence,  by  formula  419, 
fF=C^  =.582x110  =  64. 03  watts.     Ans. 

{c)  By  solution  {a\  C=.582  ;  R-  189.06  ;  /  =  1  second  ;  hence,  by 
formula  418,  the  number  of  British  Thermal  Units, 

H=  .0009477  C^  Rf  =  .0000477  X  .582  X  .582  X  189.06  X  1  = 
.0607  B.  T.  U.     Ans. 

{d)  By  solution  {b),  the  lamp  consumes  64.02  watts.  According  to 
formula  422,   1  horsepower  =  746  watts  ;  hence,   1  horsepower  will 

supply  -TTi-^  =  about  12  such  lamps.     Ans. 
'^^  ■'    64.02 

(e)  By  solution  {c),  the  number  of  B.  T.  U.  developed  per  second  = 
.060718.  By  Table  78,  1  B.  T.  U.  =  778  foot-pounds  ;  hence,  .060718 
B.  T,  U.  =  .0607  X  "^"^S  =  47.22  foot-pounds  per  second.     Ans. 

(/)  According  to  Art.  2357,  1  K.W.  =1,000  watts;  hence,  10 
K.  W.  =  10  X  1,000  =  10,000  watts.     But  by  solution  (d),  1  lamp  requires 

64.02  watts  ;    hence,  10  K.  W,  will  suffice  for    ^^^^  =  about  156  such 

lamps.    Ans. 


ELECTRICITY  AND  MAGNETISM.  1517 

EXAMPLES  FOR  PRACTICE. 

1.  Find  the  rate  of  doing  work  in  watts  when  a  current  of  40  amperes 
flows  against  a  resistance  of  2+  ohms.  Ans.  4,000  watts. 

2.  Express  the  rate  of  doing  work  in  horsepower  units  when  a  cur- 
rent of  electricity  loses  a  potential  of  20  volts  in  passing  through  a 
resistance  of  1  ohm.  Ans.  .5362  horsepower. 

3.  How  many  watts  in  4.5  horsepower  ?  Ans.  3,357  watts. 

4.  The  power  in  an  electric  circuit  is  equivalent  to  4  horsepower. 
If  a  current  of  30  amperes  is  flowing,  what  is  the  electromotive  force 
developed  ?  Ans,  99.4667  volts. 

MAGNETISM. 


NATURAL  MAGNETS. 

2358.  Near  the  town  of  Magnesia,  in  Asia  Minor,  the 
ancients  found  an  ore  which  possessed  a  remarkable  attract- 
ive power  for  iron.  This  attractive  power  they  named 
magnetism,  and  a  piece  of  ore  having  this  power  was 
termed  a  magnet.  The  ore  itself  has  since  been  named 
magnetite,  and  has  been  found  to  be  a  chemical  combina- 
tion of  about  72  parts  of  iron  and  28  parts  of  oxygen,  by 
weight. 

2359.  A  still  more  remarkable  discovery  was  made 
concerning  this  ore.  It  was  found  that  when  a  piece  of  the 
ore  was  hung  from  a  thread,  it  invariably  swung  around  to 
such  a  position  that  one  of  its  ends  pointed  north  and  the 
other  south.  It  was  also  observed  that  the  same  end  always 
pointed  north.  Due  to  this  fact,  small  pieces  of  the  ore  so 
suspended  were  used  in  navigation.  Ships  could  be  steered 
in  any  direction  by  its  aid,  because  the  direction  of  the 
north  was  always  shown  by  one  end  of  the  stone.  From 
this  fact  the  name  lodestone  (meaning  ^''leading  stone"') 
was  given  to  the  natural  ore. 


ARTIFICIAL  MAGNETS. 
2360.  When  a  bar  or  needle  of  hardened  steel  is 
rubbed  with  a  piece  of  lodestone,  it  acquires  magnetic  prop- 
erties similar  to  those  of  the  lodestone,  without  the  latter 
losing  any  of  its  own  magnetism.  Such  bars  are  called 
artificial  magnets. 


1518 


PRINCIPLES  OF 


Artificial  magnets  which  retain  their  magnetism  for  a 
long  time  are  called  perinanent  magnets. 

The  common  form  of  artificial  magnets  is  a  bar  of  steel 
bent  into  the  shape  of  a  horseshoe  and  then  hardened  and 
magnetized.  A  piece  of  soft  iron  called  an  armature,  or 
keeper,  is  placed  across  the  two  free  ends,  which  helps  to 
prevent  the  magnet  from  losing  its  magnetism. 

2361.  If  a  bar  magnet  is  dipped  into  iron  filings,  the 
filings  are  attracted  towards  the  two  ends  and  adhere  there 
in  tufts,  while  towards  the  center  of  the  bar,  half  way 
between  the  ends,  there  is  no  such  tendency.  (See  Fig.  918.) 


Fig.  918. 

That  part  of  the  magnet  where  there  is  no  apparent  mag- 
netic attraction  is  called  the  neutral  line,  and  the  parts 
around  the  ends  where  the  attraction  is  greatest  are  called 
poles.  An  im^aginary  line  drawn  through  the  center  of  the 
magnet  from  end  to  end,  connecting  the  two  poles  together, 
is  termed  the  axis  of  magnetism. 

2302.  The  magnetic  compass  consists  of  a  mag- 
netized steel  needle,  Fig.  919,  resting  upon  a  fine  point,  so 
as  to  turn  freely  in  a  horizontal  plane. 
When  not  in  the  vicinity  of  other  mag- 
nets or  magnetized  iron,  the  needle  will 
always  come  to  rest  with  one  end 
pointing  towards  the  north  and  the 
other  towards  the  south.  The  end 
pointing  northwards  is  the  north-seek- 
ing pole,   commonly  called  the  north 


Fig.  919. 


ELECTRICITY  AND  MAGNETISM.  1519 

pole,  and  the  opposite  end  is  called  the  soutti  pole.     This 
polarity  applies  as  well  to  all  magnets. 

2363.  If  the  north  pole  of  one  magnet  is  brought  near 
the  south  pole  of  another  magnet,  attraction  takes  place  ; 
but  if  two  north  poles  or  two  south  poles  are  brought 
together,  they  repel  each  other.  In  general,  like  magnetic 
poles  repel  one  aiiotJier  ;  tinlike  poles  attract. 

)2364.  The  earth  is  a  great  magnet  whose  magnetic 
poles  coincide  nearly  but  not  quite  with  the  true  geographi- 
cal north  and  south  poles.  By  the  laws  of  attraction  and 
repulsion,  given  in  Art.  3363,  it  is  seen  why  a  freely  sus- 
pended magnet,  therefore,  will  always  point  in  a  north-south 
direction. 

2365.  It  is  impossible  to  produce  a  magnet  with  only 
one  pole.  If  a  long  bar  magnet  is  broken  into  any  number 
of  parts,  each  part  will  still  be  a  magnet  and  have  two  poles, 
a  north  and  a  south. 

2366.  Magnetic  substances  are  those  substances 
which  are  not  in  themselves  magnets,  that  is,  they  do  not 
possess  poles  and  neutral  lines,  but,  nevertheless,  are  capa- 
ble of  being  attracted  by  a  magnet.  A  piece  of  soft  iron 
will  attract  either  pole  of  a  magnet,  or  will  itself  be 
attracted  towards  a  pole  of  a  magnet,  but  when  not  in  the 
vicinity  of  a  magnet  it  has  no  defined  poles.  In  addition 
to  iron  and  its  alloys,  the  following  metals  are  magnetic 
substances:  nickel^  cobalt^  manganese^  cerium^  daxdicJiromiiun. 
These  metals,  however,  possess  magnetic  properties  in  a 
very  inferior  degree,  compared  with  iron  and  its  alloys.  All 
other  known  substances  are  called  non-magnetic  substances. 

2367.  The  space  surrounding  a  magnet  is  called  a 
magnetic  field ;  or,  in  other  words,  a  magnetic  field  is  a 
place  where  a  freely  suspended  magnetic  needle  will  always 
come  to  rest  pointing  in  the  same  direction. 


1520 


PRINCIPLES  OF 


2368. 

to    act    in 


MAGNETIC  LINES  OF  FORCE. 

Magnetic  attractions  and  repulsions  are  assumed 

a  definite   direction   and  along   imaginary  lines 

called  lines  of  magnetic  force, 

or  simply  lines  of  forxe.  Their 
position  in  any  plane  may  be 
shown  by  placing  a  sheet  of  paper 
over  a  magnet,  and  sprinkling  fine 
iron  filings  over  the  paper.  In 
the  case  of  a  bar  magnet  lying  on 
its  side,  the  iron  filings  will  ar- 
range themselves  in  curved  lines 
Fig.  920.  extending  from   the  north  to  the 

south  poles,  as  shown  in  Fig.  920.  A  view  of  the  magnetic 
field  looking  towards  either  pole  of  a  bar  magnet  would 
exhibit  merely  radial  lines,  as  shown  by  the  iron  filings  in 
Fig.  921. 

Every  line  of  force  is  assumed  to  pass  out  from  the  north 
pole,  make  a  complete  circuit 
through  the  surrounding  medium, 
and  return  into  the  south  pole; 
from  thence  through  the  magnet 
to  the  north  pole  again,  as  shown 
in  Fig.  922. 

This  is  called  the  direction  of 
the  lines  of  force,  and  the  path 
which  they  take  is  called  the  mag- 
netic circuit.  Every  line  of 
force  forms  a  complete  magnetic 
circuit  by  itself. 

The  direction  of  the  lines  of  force  in  any  magnetic  field 
can  be  traced  by  a  small  freely  suspended  magnetic  needle, 
or  a  small  compass  such  as  is  shown  by  in  in  Fig.  922.  The 
north  pole  of  the  needle  will  always  point  in  the  direction  of 
the  lines  of  force,  the  length  of  the  needle  lying  parallel  or 
tangent  to  the  lines  of  force  at  that  place.  If  the  needle  be 
moved  bodily  in  the  direction  towards  which  its  north  pole 
points,  its  center  or  pivot  will  describe  a  path  coinciding 


11 '",'^///^ 


Fig.  921. 


ELECTRICITY  AND  MAGNETISM. 


1521 


with  the  direction  of  the  lines  of  force  along  that  part  of  the 
magnetic  field.  In  Fig.  922  the  arrow-heads  indicate  the 
direction  of  the  lines  of  force.  It  will  be  noted  that  in 
Figs.  930,  921,   and  923,   the  magnetic  lines  are  shown  in 


— <t 

Fig.  923. 


one  plane  only,  namely,  in  the  plane  of  the  paper.  It  should 
be  borne  in  mind,  however,  that  they  extend  out  from  the 
magnet  in  every  direction,  above,  below,  and  to  both  sides. 


MAGNETIC  CIRCUITS. 

2369.  The  lengtJi  of  a  magnetic  circuit  represents  the 
average  lengths  of  all  the  lines  of  force  measured  from 
where  they  pass  out  from  the  north  pole  along  their  circuit 
through  the  surrounding  medium  to  where  they  enter  the 
south  pole,  plus  their  length  in  the  magnet.  In  a  short 
bar  magnet,  the  length  of  the  magnetic  circuit  may  be 
exceedingly  large  and  difficult  to  measure,  because  a  great 


1523 


PRINCIPLES  OF 


many  of  the  lines  of  force  will  travel  a  long  distance  before 

entering    the    south  pole.      In  a  longer  bar,  however,  bent 

into  the  shape  of  a  horseshoe,  the 
lines  of  force  pass  out  from  the 
north  pole  and  enter  the  south 
pole  immediately,  thus  making 
the  average  length  of  the  mag- 
netic circuit  comparatively  short 
and  easy  to  determine.  Lines  of 
force  can  never  intersect  each 
other;  when  two  opposing  mag- 
netic fields  are  brought  together, 
Fig.  923.  the  lines  of  force  from  each  will  be 

crowded  and  distorted  from    their  original    direction  until 

they  coincide  in  direction  with  those  opposing  and  form  a  re- 
sultant field,  in  which  the  direction 

of  the  lines  of  force  will  depend 

upon    the    relative    strengths    of 

the  two  opposing  magnetic  fields. 

The  action  of  the    lines  of   force 

when     opposing     each     other    in 

direction    is    shown    in    Fig.    923 

and   Fig.  924,  by  the  aid    of  iron 

filings. 

The  resulting  poles  thus  formed 

are  called  consequent  poles.  fig.  924. 

2370.  In  every  magnetic  field  there  are  certain  stresses 
which  produce  a  tension  along  the  lines  of  force  and  a  pres- 
sure across  them ;  that  is,  the  magnetic 
lines  tend  to  shorten  themselves  from 
end  to  end,  and  repel  one  another  as 
they  lie  side  by  side. 


2371.     A  simple  magnetic  cir- 
cuit is  one  composed  of  some  magnetic 
substance  having  a   uniform   sectional 
Fig.  925.  area  throughout   its   entire  length,  as 

shown  in  Fig,  925,  which  represents  a  simple  ring. 


ELECTRICITY  AND  MAGNETISM.  1523 

2372.  A  compound  magnetic  circuit  is  a  circuit  in 
which  the  lines  of  force  pass  consecutively  through  several 
different  kinds  of  magnetic  or  non- 
magnetic substances.  Fig.  926 
represents  a  compound  magnetic 
circuit  in  which  the  lines  of  force 
pass  through  two  halves  of  an  iron 
ring  and  across  two  air-gaps. 


2373.  A  closed  magnetic 
circuit  is  a  circuit  composed  en- 
tirely of  magnetic  substances,  and 
in  which  the  lines  of  force  do  not  ^'-^°-  ^'^^■ 

pass  across  an  air-gap,  A  c/oscd  magnetic  circuit  may  some- 
times .be  a  compound  one,  as  would  be  the  case,  for  instance, 
in  Fig.  926  if  the  air-gaps  there  shown  were  filled,  say,  with 
cobalt,  or  any  of  the  substances  mentioned  in  Art.  2366. 

2374.  The  sectional  area  of  a  magnetic  circuit  at 
any  point  is  the  area  of  a  jalane  through  which  the  lines  of 
force  pass,  the  plane  being  taken  i^erpendicularly  to  their 
direction  at  that  point.  In  a  rectangular  bar  magnet,  the 
sectional  area  of  the  magnetic  circuit  at  the  neutral  line 
will  be  the  sectional  area  of  the  bar  at  that  line,  or  the 
breadth  of  the  magnet  multiplied  by  its  thickness. 

The  sectional  area  of  the  magnetic  circuit  outside  the 
magnet  would  be  an  indeterminate  quantity,  because  the 
lines  of  force  spread  apart  and  diverge  in  all  directions 
before  entering  the  south  pole.  But  where  the  lines  of  force 
have  only  a  small  air-gap  to  pass  across,  as  in  Fig.  923,  the 
tendency  to  spread  apart  will  be  less,  and  the  sectional  area 
of  the  magnetic  circuit  may  be  taken  as  the  area  of  the 
polar  face. 

For  example,  the  sectional  area  of  the  magnetic  circuit  in 
a  bar  magnet  .5  inch  wide  by  .25  inch  thick  is  .5  X  .25  = 
.125  square  inch ;  that  of  a  round  bar  magnet  1  inch  in  diam- 
eter is  I''  X  .7854  =  .7854  square  inch,  since  the  area  of  a 
circle  is  equal  to  its  diameter  squared  multiplied  by  .7854. 


1524  PRINCIPLES  OP 

MAGNETIC   INDUCTION. 

2375.  When  a  magnetic  substance  is  brought  Into  a 
magnetic  field,  that  is,  in  the  neighborhood  of  a  magnet,  so 
that  the  lines  from  the  magnet  reach  it,  the  substance  also 
immediately  becomes  magnetic.  The  lines  of  force  emana- 
ting from  the  magnet  and  reaching  the  substance  crowd 
together  and  tend  to  pass  through  the  substance.  The  sub- 
stance so  magnetized  is,  however,  only  a  temporary  magnet. 
When  it  is  again  removed  from  the  magnetic  field,  its  mag- 
netism disappears.  While  under  the  influence  of  the  mag- 
net, however,  it  behaves  as  does  any  other  magnet,  and  has 
polarity,  but  this  polarity  is  so  distributed  in  the  substance 
that  its  south  pole  is  that  pole  where  the  magnetic  lines 
coming  from  the  magnet  enter  it,  while  its  north  pole  is  in 
that  portion  of  the  substance  where  the  magnetic  lines 
leave  it.  The  production  of  magnetism  in  a  magnetic  sub- 
stance in  this  manner  is  called  magnetic  induction.  The 
production  of  artificial  magnetism  in  a  hardened  steel  needle 
or  bar  by  contact  with  a  lodestone  is  only  a  special  case  of 
magnetic  induction. 

2376.  The  amount  or  quantity  of  magnetism  is 

expressed  by  the  total  number  of  niagnetic  lines  of  force 
passing  along  the  magnetic  circuit.  In  a  bar  magnet,  for 
instance,  the  quantity  of  magnetism  would  be  that  number 
of  lines  which  pass  through  the  metal  from  pole  to  pole,  and 
which,  if  the  magnet  is  imagined  cut  through  at  the  neutral 
line,  would  pass  through  the  surfaces  thus  produced. 

2377.  If  this  surface  is  divided  into  unit  areas,  for  in- 
stance square  inches,  then  the  number  of  magnetic  lines 
passing  through  each  such  unit  of  area  is  termed  the  mag- 
netic density  of  the  substance. 

Magnetic  density  is,  therefore,  the  number  of  lines  of 
force  passings  through  a  unit  area  measured  perpendicularly 
to  their  direction. 

The  length  of  the  magnetic  circuit  does  not  affect  the 
magnetic  density  in  that  circuit  so  long  as  the  total  number 
of  lines  of  force  remains  unchanged. 


ELECTRICITY  AND  MAGNETISM.  1525 

To  find  the  magnetic  density  per  square  inch  when  the 
sectional  area  of  the  magnetic  circuit  and  the  total  number 
of  lines  of  force  are  known, 

Let  N  =  total  number  of  lines  of  force; 

A  =  sectional    area   of    magnetic    circuit    in    square 

inches; 
B  =  magnetic  density  per  square  inch. 

Then,  ^=T  (427.) 

That  is  to  say,  t/i^  magnetic  density  in  lines  of  force  per 
square  inch  is  obtained  by  dividing  tJie  total  member  of  lines 
of  force  by  the  sectional  area  of  the  magnetic  circuit  in  square 
inches. 

For  example,  after  measuring  the  magnetism  in  a  straight 
bar  magnet  \  inch  square  and  of  any  length,  the  total 
amount  of  magnetism  at  the  neutral  line  is  found  to  be 
25,000  lines  of  force.     The  magnetic  density  in  the  bar  is, 

therefore,  by  formula  427,  B  =  ^  =  ^^^^  =  100,000  lines 

of  force  per  square  inch.  This  is  equivalent  to  saying  that 
100,000  lines  of  force  would  pass  through  the  magnet  if  its 
sectional  area  were  increased  to  1  square  inch  and  the  lines 
of  force  were  increased  in  the  same  proportion. 

The  total  magnetism  in  a  horseshoe  magnet  made  of  a  bar 
of  iron  \\  inches  square  is  90,000  lines  of  force.  The 
magnetic  density  in  the  bar  is,  therefore,  by  formula  427, 

„         N  90,000  ,^  ^^^   1-  r  r  •       t. 

B  =  ^-  =  — — r  =  40,000  Imes  of  force  per  square  inch 

J±        1. 5  X  !•  5 

That  is,  40,000  lines  of  force  would  pass  through  the  magnet 

if  its  sectional  area  were  reduced  to  1  square  inch,  and  the 

lines  of  force  were  reduced  in  the  same  proportion. 

2378.  To  find  the  total  number  of  lines  of  force  in  a 
magnetic  circuit  when  the  sectional  area  of  the  magnetic 
circuit  and  the  magnetic  density  at  that  point  are  known, 
use  the  notation  of  Art.  2377,  giving 

N=A^.         (428.) 


1526  PRINCIPLES  OF 

That  is  to  say,  tlie  total  number  of  lines  of  force  in  a  mag' 
netic  circuit  is  obtained  by  multiplying  the  sectional  area  in 
square  incites  by  the  magnetic  density  per  square  inch. 

Example. — In  a  certain  part  of  a  magnetic  circuit  the  cross-section 
is  .75  inch  X  -5  inch,  and  the  magnetic  density  at  that  point  is  50,000 
lines  of  force  per  square  inch ;  find  the  total  number  of  lines  of  force 
in  the  magnetic  circuit. 

Solution. — The  sectional  area  of  the  magnetic  circuit  is  ^4  =  .75  X 
.5  =  .375  square  inch.  By  formula  428,  the  total  number  of  lines  of 
force  =  A^=  ^  B  =  .375  X  50,000  =  18,750  lines  of  force.     Ans. 

Example. — The  cross-section  of  a  magnetic  circuit  is  a  circle  1.5  inches 
in  diameter,  and  the  magnetic  density  is  20,000  lines  of  force  per  square 
inch ;  find  the  total  number  of  lines  of  force  passing  through  the  circuit. 

Solution. — Sectional  area  =  .<4  =  1.52X.7854  =  1.76715  square  inches. 
By  formula  428,  the  total  number  of  lines  of  force  —  N=.  1.76715  >. 
20,000=35,343.     Ans. 

MAGNETIC  UNITS. 

2379.  To  properly  define  the  strength  of  a  magnet 

pole,  a  unit  must  be  adopted  by  which  this  strength  can  be 
expressed.  By  universal  agreement  a  magnet  pole  having 
unit  strength  is  defined  as  a  pole  which  meets  the  follow- 
ing conditions: 

1.  It  must,  when  placed  at  a  distance  of  1  centimeter  from 
a  similar  pole  having  equal  strength  repel  this  pole  with  a 
force  of  1  dyne. 

2.  It  must,  when  placed  in  the  center  of  a  sphere  having  a 
radius  of  1  centimeter,  send  out  such  a  number  of  lines  of 
force  that  exactly  1  line  of  force  passes  through  every  squart 
centimeter  of  the  surface  of  the  sphere. 

2380.  Number  of  Magnetic  Lines  per  Unit 
Pole. — Directly  from  condition  2,  of  the  preceding  article, 
the  number  of  magnetic  lines  per  unit  pole  may  be  calcu- 
lated. It  is  there  stated  that  a  sphere  of  1  centimeter  radius 
receives  1  line  of  force  per  square  centimeter  of  surface 
when  a  unit  pole  is  situated  at  its  center.  This  is  equiva- 
lent to  saying  that  a  unit  pole  has  as  many  magnetic  lines 
as  there  are  square  centimeters  on  the  surface  of  a  sphere 


ELECTRICITY  AND  MAGNETISM.  1527 

having  a  radius  of  1  centimeter.  If  a  sphere  has  a  radius  = 
1  cm.,  its  diameter  =  2  cm.  By  the  rule  of  Art.  81  7,  area 
of  surface  =  diameter  squared  X  3.1416;  hence,  area  of  sur- 
face of  our  sphere  =  2^  X  3.1416  =  12.5664  square  centi- 
meters. But,  as  stated  before,  number  of  square  centimeters 
of  surface  equal  number  of  magnetic  lines,  whereby  we 
have  the 

Rule. — Every  magnet  pole  of  tmit  strength  has  12.5664 
-magnetic  lines. 

Note. — In  this  result,  fractions  of  magnetic  lines  appear.  Such 
fractions  of  magnetic  lines  are  often  obtained  in  magnetic  calculations. 
They  are  treated  in  tlie  same  manner  as  other  fractions  are.  Their 
significance  may  be  made  clear  by  the  following  consideration  :  Sup- 
pose we  have  a  piece  of  cloth  1  inch  wide  and  1  inch  long,  that  is, 
1  inch  square.  Let  us  further  suppose  that,  say,  13  pins  were  stuck 
vertically  into  this  cloth.  We  could  then  say  there  are  13  pins  per 
square  inch.  Assume  now  that  one  of  these  pins  was  removed,  split 
lengthAvise  in  half,  and  the  one  half  again  stuck  into  the  cloth.  Now 
we  would  say  that  there  were  only  12i,  that  is,  12.5  pins  per  square 
inch  of  cloth.  Similarly,  in  the  rule  above,  when  we  speak  of  12.5664 
magnetic  lines,  we  mean  that  a  little  over  Vl\  magnetic  lines  are  sent 
out  from  every  magnet  pole  of  unit  strength. 

2381 .  Unit  Density  of  Magnetism.— In  Art.  2377 
density  of  magnetism  was  defined  as  being  the  number  of 
lines  of  force  passing  through  unit  area.  To  express  the 
magnetic  density  definitely,  however,  we  must  have  a  unit 
whereby  to  measure  it.  This  unit  is  derived  from  condition 
2,  in  Art.  2379,  where  it  is  stated  that  a  unit  magnet  pole 
sends  1  line  of  force  through  every  square  centimeter  of  the 
surface  of  the  sphere  there  mentioned.  In  accordance  with 
this,  unit  density  of  magnetism  is  a  density  of  1  line  of  force 
per  square  centimeter.  Since  1  square  inch  equals  6.452 
square  centimeters,  this  is  equivalent  to  a  density  of  6.452 
lines  of  force  per  square  inch,  so  that  we  have  the 

Rule. —  Unit  density  of  magnetism  is  a  density  of  6.^52 
lines  of  force  per  square  inch. 

When  every  square  inch  cross-section  of  a  magnetized 
substance  has  exactly  the  same  number  of  lines  of  force 
passing  through  it,  the  magnetic  density  of  the  substance  is 
said  to  be  uniform. 


1528  PRINCIPLES  OF 

When  this  is  not  the  case,  the  density  is  said  to  be  non- 
uniform. 

2382.  Relation  Bet^veen  Electrical  and  Mag- 
netic Units. — In  Art.  2379  a  magnet  pole  of  unit 
strength  is  defined  as  exerting,  under  the  condition  stated, 
a  force  of  1  dyne.  In  Art.  2262,  however,  the  dyne  is 
given  as  the  fundamental  unit  of  force  in  general.  This 
fact  makes  it  possible  to  compare  magnetic  forces  to  both 
electrical  and  mechanical  forces ;  for 
1  dyne  =  unit  of  magnetic  force; 
1  dyne  =  unit  of  force  in  general  (see  Art.  2262). 

1  dyne  exerted  through  1  centimeter  =  1  dyne  cm.  =  1 
erg  =  unit  of  work  (Art.  2263). 

10,000,000  ergs  =-1  joule  =  unit  of  electrical  work  (Art. 
2330). 

1.356  joules  =  1  foot-pound  =  unit  of  mechanical  work 
(Arts.  2333  and  2348). 

We  thus  have  given  the  relation  between  dynes,  ergs, 
joules,  and  foot-pounds,  or,  in  other  words,  the  relation 
between  force  and  work  for  magnetic,  electrical,  and 
mechanical  quantities. 

Example. — Two  similar  magnet  poles  3  centimeters  apart  repel  each 
other  with  a  force  o^  4  dynes,  {a)  How  many  ergs  of  work  must  be 
expended  to  bring  the  one  pole  up  to  the  other  one  against  this  repul- 
sion ?    (i)  How  many  foot-pounds  of  work  is  this  equivalent  to  ? 

Solution. — {a)  To  bring  one  pole  up  to  the  other  through  a  distance 
of  3  centimeters,  a  force  of  4  dynes  must  be  overcome  through  a  dis- 
tance of  3  centimeters.  By  Art.  3263,  the  work  done  equals  4x3  = 
12  dyne  centimeters,  or  12  ergs.     Ans. 

{d}  By  Art.  2330,  1  joule  =  10,000,000  ergs  ;  hence,  1  erg  = 
.0000001  joule.  By  solution  (a)  the  work  done  is  12  ergs  =:  12  X 
.0000001  =  .0000012  joule.  By  Art.  2346,  Table  78,  1  joule  =  .7373 
foot-pound.  Hence,  the  work  done  in  foot-pounds  equals  .0000012  X 
.7373  -  .00000088476  foot-pound.     Ans. 


ELECTROMAGIVETISM. 
2383.     If  a  conductor  conveying  a  current  of  electricity 
be  brought  near  a  freely  suspended  magnetic  needle,  the  nee- 
dle will  tend  to  place  itself  at  right  angles  to  the  conductor, 
as  indicated  by  the  arrows   in    Fig.   927  ;    or,   in    general, 


ELECTRICITY  AND  MAGNETISM. 


1529 


an  electric  current  and  a  magnet  exert  a  mutual  force  upon 
each  other.     From  the  definition  given  in  Art.  2367,  the 


^ 


Fig.  927. 

Space  surrounding  the  conductor  is  a  magnetic  field.  If  the 
conductor  is  threaded  up  through  a  piece  of  cardboard,  and 
iron  filings  are  sprinkled  on  the 
cardboard,  they  will  arrange  them- 
selves in  concentric  circles  around 
the  wire,  as  shown  in  Fig.  928. 
This  effect  will  be  observed 
throughout  the  whole  length  of 
the  conductor,  and  is  caused  en- 
tirely by  the  current.  In  fact, 
every  conductor  conveying  a 
t  current    of     electricity 

can     be     imagined     as 

completely    surrounded 


>;;;n^<o^  ■  -~*=-i 


Fig.  929. 


Fig.  928. 
by   a   sort   of    magnetic 
zuhirl,  as  shown  in  Fig.  929,  the  magnetic  density 
decreasing   as   the  distance   from  the    conductor 
increases. 

2384.  If  the  current  in  a  horizontal  conduct- 
or is  flowing  tozvards  the 
north  and  a  compass  is  placed 
under  the  wire,  the  north  pole 
of  the  needle  will  be  deflected 
towards  the  w^i'^'/  by  placing 
the  compass  over  the  wire, 
the  north  pole  of  the  needle 
will  be  deflected  towards  the 
east.   (See  Fig.  930.)    Reverse  fig.  930. 


1530 


PRINCIPLES  OF 


the  direction  of  the  current  in  the  conductor,  and  the 
needle  will  point  in  the  opposite  direction  in  each  case  re- 
spectively. 

If  the  conductor  is  placed  over  the  needle  and  then  bent 

back  under  it,  forming  a  loop, 
as  shown  in  Fig.  931,  the  ten- 
dency of  the  current  in  both 
top  and  bottom  portions  of 
the  wire  is  to  deflect  the  north 
pole  of  the  needle  in  the  same 
direction.  From  these  experi- 
ments, knowing  the  direction 
of  current  in  the  conductor, 
Fig.  931.  the  following  rule  is  deduced 

for  the  direetion  of  the  lines  of  force  around  the  conductor: 

Rule. — If  the  current 
is  flowing  in  the  conduct- 
or away  from  the  observ- 
er, then  the  direction  of 
the  lines  of  force  zvill  be 
around  the  conductor  in 
the  clirection  of  the  ]iands 
of  a  watch. 

The  direction  of  the 
lines  of  force  around  a 
conductor  is  shoAvn  by 
the  arrow-heads  and 
compass  needles  in  Fig. 
932,  where  the  current  is 
assumed  to  be  flowing 
downwards,  or  away  from 
the  observer. 


Fig.  932. 


ELECTRICAL    APPARATUS. 

2385.  The  following  is  a  description  of  the  free  electrical  appa- 
ratus with  which  the  student  is  furnished  in  connection  with  this 
Course.  Directions  are  given  for  performing  certain  experiments  cal- 
culated to  help  the  student  to  a  better  understanding  of  the  subject 


ELECTRICITY  AND  MAGNETISM. 


1531 


treated.  Unless  the  student  has  had  previous  instruction  of  a  like 
nature,  he  is  earnestly  requested  (though  not  required)  to  make 
all  the  experiments  mentioned,  and  to  keep  a  record  of  his  results 
by  answering  the  questions  under  the  heading  Experiments  with 
Electrical  Apparatus,  which  follows  this  description  of  the  same.  He 
may  forward  his  record  to  the  School,  if  he  so  desires,  for  correc- 
tion  and  approval,  when  he  sends  his  answers  to  the  questions  on  this 
subject,  but  he  will  be  marked  and  his  work  computed  in  connection 
with-  his  work  on  the  questions  above  referred  to. 


DESCRIPTION  OF  APPARATUS. 

2386.  The  cell  illustrated  in  Fig.  933  is  of  an  im- 
proved LeclancJic  type.  It  is  quite  similar  to  the  simple  cell 
described  in  Art.  2240. 
The  electrolyte  is  a  solu- 
tion of  ammonium  chlo- 
ride (sal  ammoniac) ;  the 
positive  element  is  a  piece 
of  rolled  zinc  Z,  and  the 
negative  element  is  a  block 
of  carbon  C.  To  prevent 
the  formation  of  hydrogen 
that  occurs  in  the  simple 
cell,  the  carbon  block  is 
enclosed  in  a  cup  P,  made 
of  porous  clay,  and  the 
space  between  the  cup  and 
the  carbon  is  filled  with 
a  substance  (peroxide,  or 
black  oxide,  of  manganese) 
with  which  the  hydrogen 
formed  when  the  cell  is  in 
action  combines.  Direc- 
tions for  setting  up  the  cell  accompany  each  one ;  the  proper 
amount  of  sal  ammoniac  for  one  charge  is  also  sent  with 
each  cell.  The  cell  is  connected  to  the  external  circuit  by 
clamping  the  bared  ends  of  the  connecting  wires,  one  under 
the  brass  thumb-nut  B^  the  other  in  the  hole  in  the  zinc 
electrode  by  means  of  the  thumb-screw  B^. 


Fig.  933. 


1532  PRINCIPLES  OF 

Before  setting  up  the  cell,  unscrew  the  brass  thumb-nut  B 
from  the  top  of  the  carbon  electrode,  and  scrape  away  what- 
ever paraffin  or  black  wax  there  may  be  on  the  thumb-nut, 
its  screw,  or  the  surface  upon  w^hich  the  nut  bears  when 
screwed  up  tight. 

When  properly  set  up,  this  cell  will  give  an  E.  M,  F.  of 
about  1.5  volts. 

A  full  description  of  the  principles  upon  which  this  cell 
acts  will  be  given  in  the  section  on  "  Batteries." 

The  compass  consists  of  a  brass  case  with  a  thick  glass 
top,  in  which  a  strongly  magnetized  steel  needle  is  suspended 
on  a  steel  pivot;  beneath  the  needle  is  a  scale  which  shows 
the  eight  principal  points  of  the  compass,  and  is  also  divided 
around  the  edge  into  180  divisions,  each  division,  therefore, 
having  a  value  of  two  degrees;  by  these  divisions  the  angle 
between  any  two  positions  of  the  needle  may  be  read. 

In  estimating  such  an  angle,  care  should  be  taken  to  look 
down  on  the  needle  vertically,  so  that  the  point  of  the 
needle  will  appear  directly  over  the  proper  degree  mark. 
With  a  little  practice,  the  position  of  the  needle  should  be 
read  within  one  degree,  or  even  less. 

The  bar  magnet  is  a  piece  of  strongly  magnetized  hard- 
ened steel,  h\  in.  X  f  in.  In  one  end  is  a  tapped  hole,  in 
which  is  a  screw;  the  use  of  this  little  attachment  will  be  ex- 
plained later  in  the  Course ;    hence,  it  should  not  be  mislaid. 

The  horseshoe  magnet  is  also  a  piece  of  hardened  steel, 
which  was  bent  to  a  horseshoe  form  before  being  hardened 
and  magnetized.     One  pole  has  a  mark  across  it  near  the  end. 

The  small,  soft  wrought-iron  keeper  supplied  with  the 
magnet  should  be  kept  across  the  poles  when  the  magnet  is 
not  in  use,  as  this  tends  to  keep  the  strength  of  the  magnet 
more  permanent. 

Striking  the  magnets  with  any  hard  substance,  dropping 
them,  or  heating  them  to  more  than  about  570°  F. ,  should  be 
avoided,  as  the  result  would  be  that  they  would  lose  some  or 
all  of  their  magnetic  force. 

The  iron  filings  need  no  description ;  their  use  in  con- 
nection with  the  magnets  will  be  given  in  connection  with 
the  description  of  the  experiments. 


ELECTRICITY  AND  MAGNETISM. 


1533 


The  wire  supplied  is  No.  18  B.  &  S.  gauge  (.040"  diam.) 
copper  wire,  insulated  with  two  layers  of  cotton  soaked  in 
paraffin.     The  length  of  wire  in  the  coil  is  about  75  feet. 

With  the  above-named  apparatus  the  student  may  perform 
certain  experiments,  as  described  farther  on. 

2387.  Many  of  the  experiments  will  require  that  the 
circuit  be  opened  and  closed,  or  that  the  direction  of  the 
current  in  the  circuit  be  reversed.  This  may  be  done  by 
changing  over  the  connections  at  the  battery  terminals  to 
reverse  the  current,  or  by  simply  disconnecting  one  wire  to 
break  the  circuit. 

A  switch  which  may  be  used  for  such  purposes  is  much 
more  convenient,  and  should  be  prepared,  if  possible. 

A  cheap  and  simple  switch,  which  will  answer  the  above 
requirements,  may  be  easily  made  with  the  following 
materials: 

1  piece  of  pine  board  about  3  in.  X  5  in.  X  |-  in. 

1  piece  of  wood  about  |-  in.  X  f  in.  X  3  in. 

9  round-head  brass  wood  screws,  f  in.,  No,  8. 

2  round-head  brass  wood  screws,  |-  in.,  No.  6. 
12  copper  washers  with  •r6--in.  hole. 

2  strips  of  brass  about  ^  in.  wide,  -^-^  in.  thick,  and  4^  in, 
long,  each  with  a  -f-Q-in.  hole  f  in.  from  each  end. 
Some  short  pieces  of  the  insulated  wire. 


Fig.  934. 
-Fig.  934  shows  the  position  of  the  screw  holes  for  the  f-in 
screws  on  the  board. 


1534 


PRINCIPLES  OF 


Fig.  935  represents  the  switch  with  the  brass  strips  in  posi- 
tion.   The  small  block  of  wood  fin.  Xf  in.  X  3  in.  is  shown  at 


Fig.  935. 

N.  The  two  brass  strips  5  and  ^S  are  fastened  to  it  by  the 
two  -l-in.No.  6  screws  V  and  K.  This  block  N  serves  to  keep 
the  two  brass  strips  equidistant,  and  also  as  a  handle  by 
which  the  switch  may  be  moved.  The  other  ends  of  the 
strips  are  held  in  place  by  the  screws  /  and  H.  These  screws 
should  be  screwed  in  tightly  enough  to  press  the  brass  strips 
down  on  the  screws  C,  D,  and  E,  when  they  are  swung  to 
one  side  or  the  other.  These  two  screws 
/  and  H  should  be  put  in  as  follows 
(see  Fig.  93G) :  Slip  the  screws  through 
one  of  the  washers  B;  then  through 
the  hole  in  one  end  of  one  of  the  brass 
strips  A  ;  then  through  another  washer 
Fig.  936.  ^^ .  then    twist    the   end    of   a   piece    of 

wire   W,  from  which  the  insulation  has  been  scraped,  loosely 
around  the  screw,  and  put  the  whole  in  place. 

The  other  end  of  the  piece  of  wire  attached  to  /should  be 
twisted  around  screw  A  before  that  screw  is  put  in,  and  the 


ELECTRICITY  AND  MAGNETISM.  1535 

other  end  of  the  piece  attached  to  H  should  be  twisted  around 
G.  These  screws  should  also  have  two  washers  each.  Screws 
C,  D,  and  E  are  simply  screwed  in  until  their  heads  are  down 
on  the  wood.  A  wire  should  connect  C  and  E  with  B  and 
D  with  E,  care  being  taken  that  where  the  wires  cross  (see 
dotted  lines  in  Fig.  935)  they  are  well  insulated  from  each 
other. 

Screws  B  and  i^  should  each  have  two  washers.  Noav,  on 
connecting  A  and  G  each  to  one  pole  of  the  battery  and 
connecting  any  other  circuit  to  B  and  E  (by  loosening  the 
screws  and  putting  the  bare  ends  of  the  wires  between  the 
two  washers  and  screwing  all  up  tight  again),  the  current 
will  flow  through  this  circuit  only  Avhen  the  brass  strips  are 
resting  either  on  (7  and  D,  or  on  D  and  E,  which  they  should 
do  with  a  good  pressure,  and  when  the  brass  strips  are 
changed  over  from  C  and  D  to  D  and  E  the  current  in  this 
circuit  will  be  reversed  in  direction,  as  will  be  seen  by  fol- 
lowing out  the  path  of  the  current  in  either  case.  In  using 
the  switch,  be  careful  that  the  brass  strips  do  not  swing 
over  to  either  side  far  enough  to  touch  screws  B  or  E. 

In  the  middle  position  of  the  strips,  as  shown  in  Fig.  935, 
the  circuit  is  open,  so  this  switch  may  be  used  either  for  a 
reversing  switch  or  a  simple  circuit-breaker.  The  screws 
A^  G,  B,  and  E  may  be  replaced  by  small  binding-posts, 
which  are  more  convenient  and  cost  little. 

It  would  be  well  to  fasten  this  switch  to  a  table  or  other 
convenient  place,  and  make  permanent  connection  between 
A  and  G  and  the  battery ;  then  any  apparatus  that  is  to  be 
used  inay  be  connected  to  the  terminals  B  and  E  of  the 
switch  without  disturbing  the  battery. 

In  the  following  pages,  wherever  it  is  stated  that  appa- 
ratus is  to  be  connected  to  the  battery,  it  is  to  be  understood 
that  the  switch,  if  made,  is  to  be  included  in  the  circuit. 

2388.  When  taking  readings  of  the  angle  of  deflection 
of  the  compass  needle,  after  the  needle  has  come  to  rest  the 
glass  should  be  tapped  lightly.  The  needle  will  then  vibrate 
a  little,  and  when  it  again  comes  to  rest  it  will  usually  be  in 


1536  PRINCIPLES  OF 

a  slightly  different  position  than  before.  This  is  due  to  the 
fact  that  when  the  needle  is  deflected,  the  slight  friction  on 
the  point  on  which  the  needle  rests  prevents  the  needle 
from  swinging  as  far  as  it  would  if  there  were  absolutely  no 
friction. 

Tapping  the  case  overcomes  this  slight  friction  by  causing 
the  needle  to  jump  a  little,  and  thus  allows  it  to  come  to 
rest  in  its  proper  position. 

As  the  resistance  of  the  No.  18  wire  is  low,  if  the  battery 
be  left  long  with  the  circuit  closed  it  is  liable  to  be  weak- 
ened; so,  after  making  the  experiments,  the  circuit  should 
be  opened  at  the  switch. 

In  making  all  experiments,  note  on  a  piece  of  paper  or  in 
a  note-book  the  apparatus  used  and  how  ;  if  necessary, 
draw  a  diagram  of  connections,  etc.  Write  down  each 
result  as  soon  as  each  part  of  the  experiment  is  completed  ; 
do  not  trust  to  meniory  for  results.  Make  all  experiments 
twice,  if  possible,  thus  checking  the  first  results.  By  taking 
the  above  precautions  and  exercising  care  in  taking  the 
readings,  reliable  and  instructive  results  may  be  obtained 
with  this  simple  apparatus  by  performing  the  experiments 
mentioned  in  the  succeeding  pages. 


EXPERIMENTS  WITH  ELECTRICAL,  APPARATUS. 

Experiment  1 . — (Arts.  2361  and  2368.)  Spread  some 
of  the  iron  filings  on  a  piece  of  paper  and  lay  the  bar  magnet 
lengthwise  on  the  filings,  {a)  Do  the  filings  change  their 
position  ?  [U)  If  so,  how  ?  [c)  If  so,  make  a  sketch  show- 
ing roughly  the  positions  assumed  by  the  filings. 

Experiment  2. — (Art.  2361.)  Take  the  magnet  up 
from  the  filings.      What  happens  to  the  filings  ? 

Experiment  3. — (Art.  2366.)  Cut  off  five  or  six 
pieces  of  the  copper  wire,  each  about  an  inch  long.  Take  five 
or  six  steel  pens,  needles,  tacks,  or  other  small  iron  or  steel 
objects,  and  mix  them  up  in  a  heap  with  the  bits  of  wire. 
Touch  the  end  of  the  bar  magnet  to  the  heap  and  note  the 
result,     {a)  Is  the  copper  wire  attracted  by  the  magnet  ? 


ELECTRICITY  AND  MAGNETISM. 


1537 


(d)  Are  the  pens  or  tacks  ?  (c)  What  sort  of  a  substance 
should  you  then  call  copjjer  ?     (d)  steel  or  iron  ? 

Experiment  4. — (Art.  2366.)  Perform  the  same  ex- 
periment with  other  substances,  and  name  the  kind  of  a 
substance  (as  regards  its  magnetic  qualities)  you  find  each 
to  be. 

Experiment  5. — (Art.  2368.)  Lay  the  horseshoe  and 
the  bar  magnets  on  the  table  in  the  position  shown  in  Fig. 
937,  making  the  dis- 
tance between  the 
two  magnets  about  -^ 
inch.     Lay  a  sheet  of  ^'°-  ^^^• 

stiff  paper  over  the  two  and  sprinkle  a./e'W  iron  filings  over 
them,  just  enough  to  show  the  direction  of  the  lines  of  force, 
tapping  the  paper  lightly  as  the  filings  are  spread  over  it. 

{a)  Make  a  sketch  showing  the  forms  assumed  by  the  iron 
filings,  (d)  What  effect  does  the  bar  magnet  have  on  the 
field  of  the  horseshoe  ? 

Experiment  6.— (Arts.   2362  and  2363.)     How  can 

you  determine  the  polarity  (a)  of  the  bar  magnet  ?  (d)  of  the 
horseshoe  magnet  ? 

Experiment  7. — (Art.  2368.)  Lay  the  horseshoe 
magnet  on  a  table  and  the  bar  magnet  beside  it,  as 
\N  shown  in  Fig.  938,  leaving  about 
1  inch  between  them.  Have  the  north 
pole  of  both  the  bar  and  the  horseshoe 
magnet  on  the  same  side  ;  spread  over 
them  a  piece  of  stiff  paper  and  sprin- 
kle on  some  iron  filings  as  before. 
(a)  Make  a  sketch  showing  the  direc- 
tion of  the  lines  of  force  of  the  field  re- 
sulting from  the  two  magnets,  as  shown 
by  the  forms  assumed  by  the  iron 
filings,  [d)  Reverse  the  bar  magnet,  i.  e.,  place  its  north 
pole  where  its  south  pole  is  in  Fig.  938  and  repeat  the  ex- 
periment, making  a  sketch  as  in  {a). 

These  formations  of  iron  filings  in  magnetic  fields  may 


Fig.  938. 


1538  PRINCIPLES  OF 

be  preserved  as  follows  :  Take  a  piece  of  window-glass  of 
suitable  size  and  heat  it  over  a  stove  or  flame  until  a  small 
piece  of  paraffin  placed  upon  it  melts.  Let  the  melted  par- 
affin spread  evenly  in  a  thin  coat  over  the  glass  plate,  and 
then  let  the  plate  cool  in  a  horizontal  position,  so  that  the 
paraffin  will  harden  in  a  layer  of  even  thickness.  When 
the  paraffin  is  hard,  place  the  plate  over  the  magnets,  suit- 
ably arranged,  and  on  the  paraffin  side  of  the  glass  sprinkle 
the  iron  filings.  Tap  the  plate  lightly  to  settle  the  filings  in 
their  places,  then  lift  the  plate  vertically  off  the  magnets 
until  beyond  their  influence.  Again  hold  the  glass  plate 
over  the  stove  or  flame  until  the  paraffin  again  melts,  taking 
pains  to  hold  the  plate  horizontally.  The  paraffin  layer  be- 
ing thin,  it  will  not  then  run,  and  the  filings  will  retain 
their  regular  positions.  When  the  paraffin  is  melted,  care- 
fully remove  the  plate  to  a  cool  spot,  and  again  let  the  par- 
affin harden.  If  these  operations  have  been  carefully  gone 
through  with,  the  filings  will  be  fastened  in  place  by  the 
paraffin  and  their  graceful  and  instructive  forms  preserved, 
making  a  permanent  record.  These  glass  plates  may  be 
used  as  negatives  and  blue-prints,  or  photographs  may  be 
printed  from  them. 

Experiment  8. — (Art.  2368.)  In  the  two  sketches 
above,  point  out  (by  marking  with  a  letter  C)  the  principal 
consequent  poles  formed. 

Experiment  9. — (Art.  2374.)  What  is  the  sectional 
area  in  square  inches  of  {a)  the  bar  magnet  ?  {li)  the  keeper 
of  the  horseshoe  magnet  ? 

Experiment  lO. — (Art.  2374.)  What  kind  of  a  mag- 
netic circuit  is  that  of  the  horseshoe  magnet  with  the  keeper 
in  place,   {a)  simple  or  compound  ?  {U)  closed  or  not  ? 

Experiment  11.— (Arts.  2237  and  2239.)  Having 
set  up  the  battery  and  let  it  stand  for  ten  or  twelve  hours, 
according  to  directions,  connect  the  two  electrodes  together 
with  a  piece  of  the  wire  five  or  six  feet  long,  taking  good 
care  that  the  bared  ends  of  the  wire  make  good  contact  with 
the  binding-posts   on  the  electrodes,      {a)  Which  way  will 


ELECTRICITY  AND  MAGNETISM.  1539 

the  current  flow  in  the  wire;  i.  e.,  from  what  to  what  ele- 
ment of  the  battery  ?  {b)  Which  is  the  positive  element  ? 
(<:)  Which  is  the  positive  electrode  ? 

Experiment  12.— (Arts.  2362  and  2364.)      Set  the 

compass  on  some  level  space,  with  no  iron  or  magnets  near. 
It  will  soon  settle  into  one  position,  {a)  Why  ?  {p)  What 
is  that  position  ? 

Experiment  13. — (Art.  2383.)  Now  take  about  a 
foot  of  the  wire  connected  to  the  battery,  between  the  two 
hands,  in  such  a  way  that  the  current  flows  from  the  right 
hand  towards  the  left  hand^  and  stand  so  that  the  wire  be- 
tween the  hands  points  north  and  south,  with  the  right  hand 
towards  the  north.  Still  keeping  the  wire  in  the  same  direc- 
tion, move  it  over  and  close  to  the  compass.  Now,  if  the 
compass  needle  does  not  move,  it  will  point  in  the  same 
direction  that  the  current  is  flowing  in  the  wire,  {a)  Does 
it  move  ?     {b')  If  so,  how  ? 

Experiment  14. — (Art.  2383.)  Cut  the  piece  of  wire 
in  the  middle  and  bare  the  ends.  Then,  taking  one  end  in 
each  hand,  touch  the  bare  ends  of  the  wire  to  sides  of  the 
brass  case  of  the  compass,  one  end  opposite  the  north  pole 
of  the  needle  and  one  opposite  the  south.  This  completes 
the  circuit  through  the  brass  case  of  the  instrument,  {a)  Is 
the  needle  affected  ?     {U)  If  so,  why  ? 

Note. — As  the  brass  case  is  lacquered,  it  will  probably  be  necessary 
to  scrape  a  little  bright  spot  at  each  point  where  it  is  desired  to  make 
contact. 

Experiment  15. — In  Art.  2384  it  is  stated  that  if  the 
current  in  a  horizontal  conductor  is  flowing  towards  the 
nortJi  and  a  compass  is  placed  under  the  wire,  the  north 
pole  of  the  needle  will  be  deflected  towards  the  west,  and 
vice  versa. 

Verify  this  by  several  experiments,  and  state  the  methods 
and  apparatus  used,  as  well  as  the  results. 

Experiment  16. — (Art.  2384.)  In  this  experiment  it 
will  be  necessary  to  wind  coils  of  wire  around  the  compass. 
In  order  to  do  this  well,  it  would  be  very  convenient  to 


1540 


PRINCIPLES  OF 


make  a  small  box  of  thin  wood,  of  the  form  and  dimensions 
shown  in  Fig.  939. 

The  ends  support  the  body  of  the  box  above  the  table  or 
other  surface  on  which  it  is  placed.  The  compass  should  be 
placed  in  the  center  of  the  box,  with  the  north  and  south 
line  of  the  divisions  on  its  scale  in  line  with  the  center  line 
of  the  box  across,  that  is,  the  line  a  b,  Fig.  939,  and  should 
be  fastened  there  by  a  drop  of  mucilage  or  other  means. 
Now,  if  the  north  and  south  lines  of  the  scale  divisions  be 
brought  into  an  actual  north  and  south  position,  as  indicated 
by  the  position  of  the  needle,  any  coil  of  wire  wound  around 


Fig.  939. 


the  box  on  the  line  a  b  will  have  its  plane  in  a  north  and 
south  position,  parallel  to  and  coinciding  with  the  axis  of 
magnetism  of  the  needle,  and  any  deflection  of  the  needle 
caused  by  a  current  in  such  a  coil  may  be  read  directly  in 
degrees  on  the  scale  of  the  instrument.  If  desired,  two  pins 
may  be  driven  into  each  edge  of  the  box  on  the  line  a  b^ 
so  that  the  wire  may  be  wound  in  between  the  pins,  insur- 
ing that  the  coil  will  be  located  correctly  with  respect  to 
the  compass. 

If  the  reversing  switch  described  in  Art.  2387  has  been 
made,  it  will  be  found  very  convenient  in  performing  the 
following  experiments.  Wind  one  single  turn  of  wire  around 
the  compass  and  send  the  current  from  the  battery  around  it. 
{a)  Is  the  needle  deflected  ?     {U)  If  so,  how  many  degrees  ? 


ELECTRICITY  AND  MAGNETISM. 


1541 


Reverse  the  current  in  the  wire,  (^r)  What  is  the  effect  ? 
Make  the  coil  of  two  turns,  {d)  Is  the  deflection  changed  ? 
How  much  ?     {e)  Why  is  the  needle  deflected  ? 


ELECTROMAGNETIC    REACTION. 

2389.  Two  parallel  conductors,  both  transmitting  cur- 
rents of  electricity,  are  either  mutually  attractive  or  repel- 
lent, depending  upon  the  relative  direction  of  their  currents. 

If  the  currents  are  flowing  in  the  same  direction  in  both 
conductors  as  represented  in  Fig.  940,  the  lines  of  force  will 
tend  to  surround  both  conductors  and  contract,  thus  attract- 
ing the  conductors.  If,  however,  the  currents  are  flowing 
In  opposite  directions,  as  represented  in  Fig.  941,  the  lines  of 


Fig.  940. 


Fig.  941. 


force  lying  between  the  conductors  will  have  the  same  direc- 
tion, and  therefore  repel  the  conductors. 


THE   SOLENOID. 

2390.  If  the  conductor  carrying  the  current  is  bent  into 
the  form  of  a  loop,  as  shown  in  Fig.  942,  then  all  the  lines 
of  force  around  the  conductor  will  thread  through  the  loop 
in  the  same  direction. 

Any  magnetic  substance,  therefore,  such  as ;//,  when  placed 
in  front  of  the  loop,  would  tend  to  place  itself  with  its 
longest  axis  projecting  into  the  loop,  that  is,  in  the  direction 
of  the  lines  of  force. 

By  bending  the  conductor  into  a  long  helix  of  several 


1542 


PRINCIPLES  OF 


loops,  the  lines  of  force  around  each  loop  will  coincide  with 
those  around  the  adjacent  loops,  forming  several  long  lines 
of  force  which  thread  through  the  entire  helix,  entering  at 
one  end  and  passing  out  through  the  other.  The  same  con- 
ditions now  exist  in  the  helix  as  exist  in  a  bar  magnet; 
namely,  the  lines  of  force  pass  out  from  one  end  and  cuter 
the  other.  In  fact,  the  helix  possesses  a  north  and  south 
pole,  a  neutral  line,  and  all  the  properties  of  attraction  and 
repulsion  of  a  magnet.     If  it  is  suspended  in  a  horizontal 


Fig.  942. 

position  and  free  to  turn,  it  will  come  to  rest  pointing  in  a 
north-south  direction. 

A  helix  made  in  this  manner  around  which  a  current  of 
electricity  is  flowing  is  called  a  solenoid. 

The  polarity  of  a  solenoid  or  the  direction  of  the  lines  of 
force  which  thread  through  it  depends  upon  the  direction  in 
which  the  conductor  is  coiled  and  the  direction  of  the  current 
in  the  conductor. 

To  determine  the  polarity  of  a  solenoid,  knowing  the 
direction  of  current: 

Rule. — In  looking  at  the  end  of  the  helix,  if  it  is  so  zuound 
that  the  current  flows  around  in  the  direction  of  the  hands  of 
a   watch,    that   end  will  be  a   south  pole ;  if  in   the  other 

direction,  it  zvill  be  a  north 
pole. 

Fig.  943  represents  a  con- 
ductor   coiled    in    a    right- 
handed   helix.      If  the  cur- 
FiG.  943.  rent  starts  to  flow  from  the 


ELECTRICITY  AND  MAGNETISM.  1543 

end  where  the  observer  stands,  that  end  will  be  a  south  pole, 
and  the  observer  will  be  looking  through  the  helix  in  the 
direction  of  the  lines  of  force. 

The  polarity  of  a  solenoid  can  be  changed   by  reversing 
the  direction  of  the  current  in  the  conductor. 


MAGNETOMOTIVE    FORCE. 

2391.  It  has  been  found  by  experiment  that  the  lines 
of  force  produced  in  a  solenoid  depend  upon  the  number  of 
turns  of  the  solenoid  and  on  the  current  circulating  therein. 
The  current  and  the  turns  together  hence  act  as  a  magnet- 
izing force.  This  magnetizing  force  is,  therefore,  equal  to 
the  product  of  current  and  turns.  When  the  current 
strength  is  given  in  amperes,  this  product  is  called  ampere- 
turns.  It  is  found  furthermore  that  the  magnetizing  force 
is  independent  of  the  size  of  the  wire,  and  that  20  amperes 
circulating  around  5  turns  and  producing  100  ampere-turns 
exert  precisely  the  same  magnetizing  force  as  1  ampere  cir- 
culating in  100  turns  or  50  amperes  in  2  turns,  all  of  which 
produce  100  ampere-turns. 

The  magnetizing  force  given  by  the  product  of  current 
and  turns  must,  however,  be  expressed  in  terms  of  the 
standard  units.  To  so  express  this  force,  the  following 
calculation  is  made: 

In  Art.  3380  it  was  shown  that  a  unit  magnet  pole 
sends  out  12.5664,  or  say  12.57  lines  of  force.  It  was  also 
shown  that  a  force  of  1  dyne  was  exerted  along  each  one  of 
these  lines;  therefore,  the  total  force  exerted  by  a  unit  mag- 
net pole  is  12.57  dynes.  Now  it  can  be  shown  that  the 
magnetic  field  produced  by  1  turn  of  wire  in  which  1  absolute 
unit  of  current  is  circulating  is  the  same  as  this;  namely, 
also  12.57  dynes.  Therefore,  any  greater  number  of  turns 
and  current  units  will  exert  a  proportionately  greater 
effect.  The  total  effect  or  magnetizing  force  is,  therefore, 
equal  to  12.57  X  current  X  turns.  To  express  this  current 
in  absolute  units,  it  is  necessary  to  divide  the  value  in 
amperes  by  IQ,      (See  Art.  2272.)     But  when  the  force  is 


1544  PRINCIPLES  OF 

expressed   in  this  manner,  it  is  termed  magnetomotive 

force  ;  so  that  we  have  the  formula 

12  57  X  ci-t 
Magnetomotive  force  = — '- — — =  1.257  X  a-t, 

where  a  =  current  in  amperes; 
t  =  number  of  turns. 
The  formula  above  is,  however,  to  be  applied  only  in  cases 
where  the  dimensions  of  the  magnetic  circuit  are  given  in 
metric  measure.  When  given  in  English  measure,  as  they 
are  throughout  the  following,  the  value  of  the  constant  is 
changed,  so  that  the  final  useful  formula  is 

Magnetomotive  force  =  3.192  X  a-t,  (429.) 

where  a  =  current  in  amperes; 
/  =:  number  of  turns. 

2392.     Intensity  of  Magnetomotive   Force. — The 

magnetomotive  force  as  given  by  formula  429  represents 
simply  the  total  magnetizing  effect  produced  by  the  solenoid. 
It  does  not  give  any  information  regarding  the  intensity  of 
this  effect  at  any  one  point;  that  is,  it  gives  no  information 
regarding  the  effect  produced  by  a  unit  length  of  such  a 
circuit.  This  is  easily  found,  however,  by  dividing  the  total 
magnetomotive  force  by  the  total  length.  The  quotient  is 
termed  the  intensity  of  magnetomotive  force,  and  is 
represented  by  the  letter  H. '  If  /  represents  the  length  of 
the  magnetic  circuit  in  inches  and  a-t  represents  the  ampere- 
turns,  then 

This  formula  shows  that  f/ie  intensity  of  magnetojnotive 
force  H  will  produce  a  tmiform  magnetic  field,  in  zvJiicJi  the 
density  will  be  H  lines  of  force  per  square  inch  of  sectional 
area  of  the  magnetic  circuit. 

This  is  equivalent  to  saying  that  the  induction  produced 
in  the  circuit  is  directly  proportional  to  the  magnetizing 
force  applied.  It  should  be  particularly  noted,  however, 
that  this  is  only  true  for  a  solenoid  in  air  or  in  other  non- 
magnetic substances.    When  a  magnetic  substance  is  brought 


ELECTRICITY  AND  MAGNETISM. 


1545 


near  such  a  solenoid,  the  effect  is  immediately  altered,  as 
shall  presently  be  shown. 

2393.  Total  Magnetic  Lines  in  a  Solenoid. — The 

total  number  of  lines  of  force  is  found  by  multiplying  the 
sectional  area  of  the  mag- 
netic circuit  in  square 
inches  by  the  value  of  H. 
For  example,  imagine  a 
coiled  conductor  of  20 
turns  bent  into  a  circular 
shape  so  that  there  are  no 
free  poles,  as  represented 
in  Fig.  944.  Each  line  of 
force  will  form  a  complete 
ring  inside  the  solenoid, 
and,  therefore,  the  length 
of  the  magnetic  circuit 
can  easily  be  measured. 
Twenty  amperes  flowing 
through  the  conductor  will 
give  a  magnetizing  force 
of  400  ampere-turns.  If  the  mean  length  of  the  magnetic 
circuit  is  5  inches,   then   by  formula   430   the    magneto- 

400 

~v 

a  uniform  magnetic  field  is  produced  in  the  solenoid  in  which 
the  density  is  255.36  lines  of  force  per  square  inch  of  sec- 
tional area.  Now,  if  the  sectional  area  of  the  magnetic  cir- 
cuit is  .5  square  inch,  there  are  .5  X  255.36  =  127.68  lines  of 
force  produced  in  the  coil.  Or,  if  the  sectional  area  is  1.5 
square  inches,  there  are  1.5  X  255.36  =  383.04  lines  of  force 
produced  in  the  coil. 

MAGNETIC    PERMEABILITY. 

2394.  In  Art.  2375  it  was  stated  that  when  a  mag- 
netic substance  is  brought  into  a  magnetic  field,  the  lines  of 
force  in  the  field  crowd  together,  and  all  try  to  pass  through 
the  substance ;  in  fact,  they  will  alter  their  circular  shape 


Fig.  944. 


motive  force  H  =  3.192  X 


255.36,   which    means    that 


1546  PRINCIPLES  OF 

and  extend  to  a  considerable  distance  from  their  original 
position  in  order  to  pass  through  it.  A  magnetic  substance, 
therefore,  offers  a  better  path  for  tlie  lines  of  force  than  air 
or  other  non-magnetic  substance. 

The  facility  afforded  by  any  substance  to  the  passage 
through  it  of  lines  of  force  is  called  magnetic  perme- 
ability, or,  simply,  permeability. 

The  permeability  of  all  non-magnetic  substances,  such  as 
air,  copper,  wood,  etc.,  is  taken  as  1,  or  unity.  The  perme- 
ability of  soft  iron  may  be  as  high  as  2,000  times  that  of 
air.  If,  therefore,  a  piece  of  soft  iron  be  inserted  into  the 
magnetic  circuit  of  a  solenoid,  the  number  of  lines  of  force 
will  be  greatly  increased,  and  the  iron  will  become  highly 
magnetized. 

THE    ELECTROMAGNET. 

2395.  A  magnet    produced    by    inserting    a    magnetic 
\  ,     substance    in  the  magnetic 

\      0K       ^      ».      0^       m.       i     circuit  of  a  solenoid    is  an 

j _ Y \..._ \ \ V \ B    electromagnet,    and    the 

\^     j        [        \       \       I        I    ^\    magnetic  substance  around 
'         I       I       \       \       \       I       i    which  the  current  circulates 
^^    V       Vr      V,      \-      V         is  called  the  core,  as  shown 
FIG.  945.  in  Fig.  945. 

In  the  ordinary  form  of  electromagnet,  the  magnetizing 
coil  consists  of  a  large  number  of  turns  of  insulated  wire ; 
that  is,  wire  covered  with  a  layer  or  coating  of  some  non- 
conducting or  insulating  material,  usually  silk  or  cotton; 
otherwise  the  current  would  take  a  shorter  and  easier  cir- 
cuit from  one  coil  to  the  adjacent  one,  or  from  the  first  to 
the  last  coil,  through  the  iron  core,  without  circulating 
around  the  magnet. 

FORMS  OF    ELECTROMAGNETS. 

2396.  The  simplest  form  of  an  electromagnet  is  the 
bar  magnet.  As  usually  constructed,  it  consists  of  a  straight 
bar  of  iron  or  steel  B  fitted  into  a  spool  or  bobbin  C  made  of 
hard  vulcanized  rubber  or  some  other  inflexible  insulating 


ELECTRICITY  AND  MAGNETISM. 


154'? 


material.  The  magnetizing  coil  of  fine  insulated  copper 
wire  w  is  wound  in  layers  in  the  bobbin,  as  shown  in 
Fig.  946. 

The  rule  for  determining  the  polarity  of  a  solenoid  (Art. 
2390)  is  the  same  for  an  electromagnet.  It  makes  no  dif- 
ference whether  the  wire  is  wound 
in  one  layer  or  in  any  number 
of  layers,  or  whether  it  is  wound 
towards  one  end  and  then  wound 
back  over  the  previous  layer 
towards  the  other;  so  long  as  the 
current  circulates  continually  in 
the  same  direction  around  the 
core,  the  polarity  of  the  magnet 
will  remain  unchanged. 

The  most  convenient  form  of 
electromagnet  for  a  great  variety  of  uses  is  the  horse- 
shoe, or  U-shaped  electromagnet.  It  consists  of  a  bar  of 
iron  bent  into  the  shape  of  a  horseshoe,  with  straight  ends, 
and   provided    with    two    magnetizing    coils,    one    on    each 

end  of  the  magnet;  the 
two  ends  which  are 
surrounded  by  the  mag- 
netizing coils  are  the 
co7'es  of  the  magnet,  and 
the  arc-shaped  piece  of 
iron  joining  them  to= 
gether  is  known  as  the 
Fig.  947.  yoke     of    the     magnet. 

The  ordinary  U-shaped  magnet,  Fig.  947,  is  made  in  three 
parts,  namely,  two  iron  cores  M  wound  with  the  magnet- 
izing coils  c  and  a  straight  bar  of  iron  b  for  a  yoke  joining 
the  two  cores  together.  In  looking  at  the  face  of  the  two 
cores,  Fig.  948,  the  current  should  circulate  aroun'd  one 
core  in  an  opposite  direction  to  that  around  the  other. 
If  the  current  circulates  around  both  cores  in  the  same 
direction,  the  lines  of  force  produced  in  the  two  cores, 
respectively,  oppose  one    another,   forming    two    like  poles 


1548 


PRINCIPLES  OP 


at  their  free  ends  and  a  consequent  pole  :n  the  yoke.     The 
total  number  of  useful  lines  of  force  produced  by  both  coils 

would,  under  these  conditions, 
be  greatly  diminished,  and  the 
magnet  would  exhibit  only  a 
small  amount  of  magnetic  at- 
traction. 

2397.  Another  common 
form  of  electromagnet  is  known 
as  the  iron-clad  electromag- 
net. In  its  simplest  form, 
Fig.  949,  it  contains  only  one 
magnetizing  coil  and  one  core. 
The  core  M  is  fastened  to  a 
disk-shaped  yoke,  and  the  mag- 
netic circuit  is  completed  through  an  iron  shell  5,  which 
rises  up  from  the  yoke  and  completely 
surrounds  and  protects  the  coil. 

2398.  Electromagnets  may  be  divi- 
ded into  three  general  classes,  according 
to  their  application,  viz. : 

1.  Those  for  lifting  weights  and  loads 
by  adhesion. 

2.  Those  for  producing  mechanical 
motion  in  an  armature  or  a  keeper ;  that  fig.  949. 

is,  for  attracting  an  armature  or  a  keeper  through   a  dis- 
tance. 

3.  Those    for   producing  a    magnetic  field    for   dynamo- 
electric  machines,  and  called  field  magnets. 


Fig.  948. 


EXPERIMENTS    WITH    ELECTRICAL,    APPARATUS. 

2399.  The  following  experiments  with  the  apparatus 
furnished  to  the  student  will  assist  in  making  clear  the  ex- 
planation given  of  the  solenoid : 

Experiment  17.— (Art.  2390.)  Coil  the  wire  into  a 
helix  of  about  \  in.  diameter  and  of  about  16  turns,     {a)  Send 


^  ELECTRICITY  AND  MAGNETISM.  1549 

a  current  from  the  battery  through  this  helix ;  will  the  end 
of  the  helix  attract  the  compass  needle  if  held  near  it  ?  (d) 
Why  ?  (c)  How  can  you  determine  beforehand  which  pole 
of  the  compass  needle  will  be  attracted  by  either  end  of  the 
helix  ? 

Experiment  18.— (Arts.  2375  and  2395.)  Place 
the  helix  on  some  support,  in  such  a  position  that  its  axis 
will  be  at  rigrht  anarles  to  the  north  and  south  line.     As  near 


Fig.  950. 

as  possible  to  one  end  of  the  helix  place  the  compass,  as 
shown  in  Fig,  950.  Send  a  current  through  the  coil  and 
note  the  deflection  of  the  compass  needle  in  degrees. 

Inside  the  coil  place  the  following  substances  and  note 
the  effect  on  the  needle,  the  current  still  circulating  in  the 
helix:  {a)  a  piece  of  wood,  as  a  pencil  or  a  few  matches;  [d) 
three  or  four  wire  nails;  (c)  the  blade  of  a  knife;  (d)  some 
brass  screws. 

Experiment  19. — (Art.  2393.)  Fasten  one  end  of 
the  helix;  place  the  compass  at  the  fixed  end  of  the  helix, 
and  on  sending  a  current  through  the  coil,  note  the  deflec- 
tion of  the  needle  in  degrees:  (1)  with  the  coils  of  the  helix 
as  close  together  as  possible,  making  the  helix  as  short  as  it 
can  be;  (2)  with  the  helix  pulled  out  to  twice  its  original 
length,  (a)  Is  there  any  difference  between  the  deflections 
in  the  two  cases  ?     [b)  How  much  ?     (c)  Why  ? 

Experiment  20.— (Arts.  2383  and  2393.)  Make  a 
helix  of  about  30  turns  and  about  the  same  diameter  as 


1550  PRINCIPLES  OF 

before.  Stretch  it  out  until  it  is  twice  its  minimum  length. 
Place  it  with  its  axis  east  and  west,  and  put  the  compass 
near  the  center  of  the  length  of  the  helix.  The  compass 
needle  will   then  point  at   right  angles  to  the  axis  of  the 


Fig.  951. 
helix,  as  shown  in  Fig.  951.  Send  a  current  through  the  helix 
and  note  the  deflection  in  degrees.  Wind  another  helix  of 
the  same  diameter  and  length  as  the  one  just  used,  but 
of  twice  the  number  of  turns,  and  place  the  new  helix  in 
the  same  relative  position  with  the  compass.  On  sending  a 
current  through  the  new  helix,  the  compass  needle  will  be 
deflected  to  a  greater  angle  than  before,  (a)  Why  ?  Move 
the  compass  away  from  the  helix,  along  a  line  at  right  angles 
to  the  axis  of  the  helix.  The  deflection  will  grow  less  and 
less,     (l;)  Why  ? 

MAGNETIZING  FORCE  AND  MAGNETIC 
DENSITY. 
2400.  The  relation  between  the  magnetizing  force  and 
the  actual  ajnount  of  magnetism  produced  in  the  core  of  an 
electromagnet  should  be  thoroughly  understood  before 
studying  the  special  designs  of  electromagnets  and  their 
uses.     It  has  been   shown  that  the  magnetic  density  pro- 


ELECTRICITY  AND  MAGNETISM.  1551 

duced  in  air  by  a  solenoid  depends  entirely  upon  the  inten- 
sity of  magjietomotive  force.  The  magnetic  density,  how- 
ever, which  is  produced  in  a  magnetic  substance  when 
placed  in  a  solenoid  depends  upon  one  other  quantity, 
namely,  the  permeability  of  the  substance.  The  permea- 
bility of  a  magnetic  substance  at  any  stage  of  magnetization 
is  a  ratio  between  the  intensity  of  the  magnetomotive  force 
acting  upon  the  substance  and  the  resulting  magnetic  den- 
sity in  the  substance.  Let  H  represent  the  intensity  of  the 
magnetomotive  force  acting  upon  a  magnetic  substance, 
and  let  B  represent  the  magnetic  density  produced  in  the 
substance,  owing  to  its  superior  magnetic  qualities.  The 
permeability  is  the  quotient  arising  from  dividing  B  by  H. 
If  /i — pronounced  imi — represents  the  permeability,  then  \i  = 

B 

— .  When  any  two  of  these  quantities  are  known,  the  third 
H 

B 
can  be  readily  found  ;  for,  transposing,  B  =  /x  H  and  H  =-— . 

If  there  is  no  magnetic  substance  in  the  core  of  the  solenoid, 

.     ,         ,  ,,       3.192  X  ampere-turns 
the  permeability  is  1  and  H  = y ■;  tnen, 

_  ,,  1  X  3.192  X  ampere-turns  3. 192  X  ampere-turns 
B=fzH  =  - J =• J : 

Hence,  H  may  be  expressed  by  saying  that  in  air  it  will  pro- 
duce a  density  of  H  lines  of  force  per  square  inch.  In 
another  case,  an  iron  ring  is  wound  with  100  turns  of  wire 
and  a  current  of  10  amperes  is  flowing  through  the  wire.  If 
the  mean  length  of  the  magnetic  circuit  in  the  ring  is  10  inches, 

^       ,           ,       ^^^               3.192  xa-t      3.192X10X100 
by    formula    430,         = j— — ■= tt: •  = 

319.2.  The  magnetic  density  produced  in  the  ring  by  this 
magnetizing  force  depends  upon  the  permeability  of  the 
iron  at  that  stage  of  magnetization.  By  the  aid  of  certain 
electrical  instruments,  which  will  be  described  in  the  section 
on  Electrical  Measurements,  the  magnetic  density  in  the 
iron  ring  can  be  determined  directly.  Suppose,  for  an  illus- 
tration, the  magnetic  density  is  found  to  be  63,840  lines  of 

R        fi3  84-0 
force  per  square  inch.     Then,  fi  =  rr=  "^Vt  ~  ^^^»  which 


1553  PklNClPLES  OP 

represents  the  permeability  of  the  iron  when  the  density  is 
63,840  lines  of  force  per  square  inch.  The  permeability, 
however,  of  a  given  magnetic  substance  changes  with  every 
stage  of  magnetization.  In  all  kinds  of  magnetic  substances, 
the  permeability  decreases  when  the  magnetism  is  increased 
beyond  a  certain  limit.  This  tendency  of  the  substance  to 
become  less  permeable  is  called  magnetic  saturation ; 
that  is,  the  substance  becomes  saturated  with  magnetism. 
A  limit  is  never  reached  where  actual  saturation  takes  place, 
but  there  is  a  limit  beyond  which  it  becomes  impracticable 
to  magnetize  the  substance.  The  practical  saturation  point 
in  wrought  iron,  soft  annealed  sheet  iron,  and  cast  steel  is 
when  the  density  is  between  120,000  and  130,000  lines  of 
force  per  square  inch.  Hence,  in  these  metals,  B  may  have 
any  value  from  0  to  130,000. 

In  gray  cast  iron  the  practical  saturation  limit  is  from 
60,000  to  70,000  lines  of  force  per  square  inch. 

The  intensity  of  magnetomotive  force  H  is  very  seldom 
carried  beyond  1,500,  and,  therefore,  H  may  have  any  value 
between  0  and  1,500. 

2401.  Before  designing  an  electromagnet  for  any  pur- 
pose, it  is  first  necessary  to  know  the  magnetic  properties 
of  the  particular  quality  of  iron  to  be  used  in  the  core — to 
find  its  permeability  at  different  stages  of  magnetization 
and  its  saturation  limit.  Tests  are  taken  upon  small  sam- 
ples of  the  metal  by  electrical  instruments,  and  the  values 
of  B,  H,  and  \i  are  calculated  from  the  readings  of  the  in- 
struments. As  these  tests  require  exceedingly  delicate  in- 
struments and  a  large  number  of  careful  measurements,  it 
is  customary  to  consult  the  results  taken  in  some  laboratory 
on  an  average  quality  of  iron  and  its  alloys.  The  results 
given  in  Tables  79,  80,  81,  and  82  have  been  found  to  agree 
very  closely  with  iron  and  steel  ordinarily  used  in  foundries 
and  machine-shops. 

Table  7-9  is  a  list  which  gives  seven  values  of  H  and  the 
corresponding  values  of  B  and  /z,  taken  on  a  piece  of  lordi- 
nary  gray  cast  iron  of  average  quality. 


ELECTRICITY  AND  MAGNETISM.  1553 

TABLE  79.  TABLE  80. 


Gray  Cast  Iron. 


Cast  Steel — Unannealed. 


B 

H 

^t 

10,000 

64 

156.3 

20,000 

105 

190.5 

30,000 

164 

182.9 

40,000 

262 

152.9 

50,000 

430 

116.3 

60,000 

718 

83.6 

65.000 

1,030 

63.1 

B 

H 

/' 

10,000 

18 

555.5 

20,000 

28 

714.3 

30,000 

35 

857.1 

40,000 

43 

930.2 

50,000 

54 

925.9 

60,000 

72 

833.3 

70,000 

99 

707.1 

80,000 

146 

547.3 

90,000 

225 

400.0 

100,000 

375 

266.6 

110,000 

730 

150.7 

115,000 

1,015 

113.3 

Table  80  gives  the  results  of  a  test  on  an  average  quality 
of  cast  steel  when  unannealed.  The  effect  of  annealing 
metals  is  to  increase  their  permeability  at  low  stages  of 
magnetization.  In  practice,  however,  it  is  found  most 
economical  to  magnetize  cast  steel  above  75,000  lines  of 
force  per  square  inch,  and  at  such  stages  of  magnetization 
annealing  has  practically  no  effect  upon  its  permeability. 

Table  81  gives  the  results  of  a  test  taken  on  sheets  .014  in. 
thick,  of  soft  annealed  charcoal  iron  of  average  quality. 

Table  82  gives  the  results  of  a  test  taken  on  an  average 
quality  of  wrought-iron  forgings. 

The  peculiarities  of  these  tests  should  be  carefully  noted. 
For  example,  it  will  be  seen  that  at  all  stages  of  magnetiza- 
tion, cast  iron  is  vastly  inferior  to  any  one  of  the  other  three 
metals.  To  produce  a  density  of  40,000  lines  of  force  per 
square  inch  in  cast  iron  requires  that  H  =  262;  whereas,  in 
cast  steel  at  the  same  density,  H  =  43,  which  indicates  that  at 
this  density  cast  iron  would  require  262  -h  43,  or  6.093  times 


1554 


PRINCIPLES  OF 


as  much  magnetizing  force  as  would  be  required  for  cast 
steel.  Therefore,  other  things  being  equal,  it  would  be 
more  economical  to  use  cast  steel  rather  than  cast  iron  for 
magnetic  purposes. 


TABLE  81. 

Sheet  Iron — Annealed. 


TABLE  82. 

Wrought-Iron  Forgings. 


B 

H 

u 

10,000 

1(3 

625.0 

20,000 

23 

869.6 

30,000 

28 

1,071.4 

40,000 

33 

1,212.1 

50,000 

42 

1,190.4 

60,000 

53 

1,132.0 

70,000 

68 

1,029.4 

80,000 

94 

851.0 

90,000 

138 

652.2 

100,000 

214 

467.3 

110,000 

374 

294.1 

120,000 

725 

165.5 

125,000 

1,075 

116.3 

B 

H 

>" 

10,000 

12.0 

833.3 

20,000 

15.0 

1,333.3 

30,000 

18.8 

1,595.7 

40,000 

23.0 

1,739.1 

50,000 

30.0 

1,666.6 

60,000 

44.0 

1,363.6 

70,000 

65.0 

1,076.9 

80,000 

104.0 

769.2 

90,000 

200.0 

450.0 

100,000 

430.0 

232.6 

105,000 

630.0 

166.6 

110,000 

1,035.0 

106.3 

CURVES  OF  MAGNETIZATION. 

2402.  The  most  convenient  mode  of  representing  the 
magnetic  qualities  of  iron  and  other  magnetic  substances  is 
to  plot  the  curves  of  magnetization  on  two  sheets  of  cross- 
section  paper.  On  one  sheet  are  plotted  saturation 
curves  which  indicate  the  relation  of  the  intensity  of  the 
magnetomotive  force  H  to  the  magnetic  density  B ;  on  the 
other  sheet  are  plotted  the  resulting  permeability  curves 
which  indicate  the  relation  of  the  permeability  \i  to  the  mag- 
netic density  B. 

The  cross-section  paper  should  be  divided  into  squares  of 
equal  dimensions  of  about  \  inch  on  a  side,  although  it  will 
be  more  accurate  if  these  squares  are  still  further  divided 


ELECTRICITY  AND  MAGNETISM. 


1555 


into  smaller  ones  yV  inch  on  a  side.     The  sheets  should  be 
at  least  11  inches  wide  by  14  inches  high. 

The  horizontal  divisions  are  called  abscissas,  and  are  in- 
dicated by  numbers  placed  in  the  margin  either  above  or 


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Fig.  952. 
below  the  chart.  The  vertical  divisions  are  called  ordi- 
nates,  and  are  represented  by  marginal  numbers  on  the 
right  or  left  hand  of  the  chart.  The  terms  abscissa  and 
ordinate,  therefore,  express  clearly  which  set  of  divisions,  the 
horizontal  or  vertical,  is  referred  to,  instead  of  designating 
the  rows  of  figures  with  reference  to  relative  position. 


1556 


PRINCIPLES  OF 


2403.  On  the  sheet  for  the  saturation  curves,  Fig.  952 
(reduced),  the  divisions  of  the  abscissas  represent  the  dif- 
ferent values  of  H,  and  each  -l-inch  division  represents  50  H. 


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Pig.  953. 

Starting  with  the  extreme  lower  left-hand  line  as  zero,  the 
remaining  lines  are  numbered  consecutively  in  units  of  50. 
The  ordinates  represent  the  different  values  of  the  magnetic 
density    B,  and   each   -^-inch    division   represents   5,000   B. 


ELECTRICITY  AND  MAGNETISM.  1557 

Starting  with  the  bottom  line  as  zero,  tne  remaining  lines 
are  numbered  consecutively  in  units  of  5,000. 

2404.  On  the  sheet  for  the  permeability  curves,  Fig. 
953  (reduced),  the  divisions  of  the  abscissas  represent  the 
different  values  of  fi  and  each  |-inch  division  represents 
100  n.  Starting  with  the  extreme  left-hand  line  as  zero,  the 
remaining  lines  are  numbered  consecutively  in  units  of  100. 
The  ordinates  represent  the  different  values  of  B,  and  are 
numbered  as  described  for  B  on  the  sheet  for  saturation  curves. 


METHOn  OF  PLOTTING  CURVES. 

2405.  In  the  first  set  of  readings  on  cast  iron.  Table  79, 
H  =  64  and  B  =  10,000.  A  dot  is  placed  on  the  bottom  line, 
Fig.  952,  representing  64  H.  The  value  B  =  10,000,  when 
pointed  off  on  the  extreme  left-hand  vertical  line,  is  repre- 
sented by  two  divisions,  and  the  point  falls  on  the  line  marked 
10,000.  This  line  is  followed  along  horizontally  until  a  point 
is  reached  which  is  directly  over  the  dot  on  the  bottom  line. 
A  heavy  dot  placed  here  will  indicate  the  combined  values 
of  B  and  H  at  the  first  readings.  The  remaining  readings 
in  Table  79  are  plotted  in  a  similar  manner,  and  afterwards 
all  the  heavy  dots  are  joined  together  by  one  long  curve. 
All  the  intermediate  values  of  H  and  the  corresponding 
values  of  B  are  now  indicated  by  the  curved  line.  For  ex- 
ample, in  the  saturation  curve  for  cast  iron,  where  H  is  350, 
the  corresponding  value  of  B  is  about  46,000  lines  of  force 
per  square  inch.  The  same  method  is  used  for  plotting  the 
rest  of  the  saturation  curves  in  Fig.  952  and  the  permeability 
curves  in  Fig.  953. 

ACCURACY  OF  CURVES. 

2406.  If  cross-section  paper  with  -l-inch  divisions  is 
used,  the  curves  should  be  plotted  and  read  with  the  help  of 
a  scale  divided  into  tenths  of  an  inch.  Under  these  con- 
ditions, points  plotted  within  -^^  of  an  inch  of  their  correct 
position  on  the  sheet  will  be  considered  as  accurate. 

All  magnetic  calculations  in  which  readings  are  used  that 


1558  PRINCIPLES  OF 

are  taken  from  the  saturation  and  permeability  curve  sheets 
will  be  considered  accurate  when  within  %.bfo  of  the  correct 
figures. 

CALCULATION  OF  THE    MAGNETIC  CIRCUIT. 

2407.  The  calculation  of  a  magnetic  circuit  is  a  more 
complicated  problem  than  that  of  the  electric  circuit,  but  the 
operation  is  much  simplified  by  treating  the  magnetic  circuit 
in  the  same  manner  as  an  electric  one  and  applying  the 
principle  of  Ohm's  law;  it  must  be  understood,  however, 
that  it  is  only  the  principle  oi  Ohm's  law  that  is  applied,  and 
not  any  of  the  actual  electrical  quantities. 

The  magnetomotive  force  has  been  described  as  that  which 
produces  the  magnetism,  but  it  will  now  be  considered  as  that 
zuhich  tends  to  drive  the  lines  of  force  along  the  magnetic 
circuit  against  a  resistance. 

The  resistance,  or  that  which  opposes  the  lines  of  force,  is 
called  reluctance,  to  distinguish  it  from  electrical  resistance. 

2408.  The  quantity  of  magnetism  or  the  total  num- 
ber of  lines  of  force  which  are  driven  along  the  magnetic 
circuit  is  called  the  induction,  and  is  found  by  dividing  the 
magnetomotive  force  by  the  reluctance.  Or,  expressed 
algebraically,  it  will  give  the  formula 

T-    1       .  magnetomotive  force 

Induction  =  • — ^^ . 

reluctance 

The  numerical  value  for  the  magnetomotive  force  is  always 
3.192  X  ampere-turns. 

2409.  The  reluctance  of  the  magnetic  circuit  depends 
upon  three  quantities:  (1)  the  length  of  the  circuit,  (2)  the 
sectional  area  of  the  circuit,  and  (3)  the  permeability  of  the 
substances  which  form  the  circuit. 

The  reluctance : 

Increases  as  the  length  of  the  magnetic  circuit  increases. 

Decreases  as  the  sectional  area  increases. 

Decreases  as  tlie  permeability  increases. 

If  /represents  the  length  of  a  magnetic  circuit  in  incheSj 


ELECTRICITY  AND  MAGNETISM.  1559 

A  its  sectional  area  in  square  inches,  and  fi  its  permeability, 
the  reluctance  of  the  circuit  can  be  expressed  by  the  formula 

Reluctance,  R  =— j-^ .  (431.) 

A  X  [J'  ' 

Writing  N  for  the  induction,  a-t  for  the  ampere-turns, 
and  substituting  the  values  cf  the  magnetomotive  force  and 
reluctance,  the  formula  for  the  magnetic  circuit,  given  in 
Art.  240S,  becomes 

N=  M^yiifi.  (432.) 

In  practice,  the  inditction,  or  the  total  number  of  lines  of 
force,  is  established  in  the  beginning  by  the  requirements  of 
the  magnet,  and,  therefore,  it  is  necessary  to  find  the  num- 
ber of  ampere-turns  required  to  drive  that  induction  along 
the  magnetic  circuit.     By  transposing,  the  ampere-turns 

The  magnetic  circuit,  however,  is  generally  a  compound 
one  ;  that  is,  it  is  composed  of  two  or  more  substances. 
The  total  reluctance  of  the  circuit  would  then  be  the 
sum  of  the  separate   reluctances  of  each  substance.      Let 

—. — 5- — ■  =  R,    be    the    reluctance    of    the    first    substance, 

—. — ^ =  R„  be    the    relucta  ice  of   the  second,  and  so   on. 

Then,  the  sum  of  the  separate  reluctances  is  R^  -|-  R^  4-  ^tc. 
Therefore,  the  ampere-turns  :?-/  are  given  by  the  formula 

ampere-turns  a-t  =  .,  X  (R ,  +  R,  -+-  etc. ).  (433.) 

2410.  After  the  dimensions  and  induction  of  a  magnet, 
have  been  established  by  the  requirements,  it  is  necessary 
to  know  the  permeabilities  jt^j,  n^,  etc.,  before  the  ampere- 
turns  can  be  calculated.  The  permeability  depends  not 
only  upon  the  kind  and  quality  of  the  magnetic  substance, 
but  also  upon  the  density  of  the  lines  of  force.     The  density 


1560 


PRINCIPLES  OP 


is  found  (see  formula  427)  by  dividing  the  total  numbei 
of  lines  of  force  which  pass  through  a  circuit  by  its  sec- 
tional area.  Consequently,  the  densities  in  the  different 
substances    which    compose   the    magnetic    circuit    will    be 

N    N 

-j—,  —^,  etc.     Then,  referring  to  the  curves  in  Fig.  953,  the 

permeability  of  any  of  the  different  metals,  corresponding 
to  their  densities,  can  be  found.  The  permeability  of  all 
non-magnetic  substances  is  always  1,  irrespective  of  the  density 
of  the  lines  of  force. 

Example. — Find  the  ampere-turns  required  to  drive  an  induction  of 
55,000  lines  of  force  through  the  circuit  of  a  horseshoe  magnet  made 


Fig.  954. 


of  cast  iron,  when  a  bar  of  wrought  iron  is  placed  across  its  two  ends, 
but  separated  from  them  by  an  air-gap  of  ^  inch.  The  dimensions  of 
the  magnet  and  bar  are  shown  in  Fig.  954. 

Solution. — This  magnetic  circuit  is  a  compound  one,  composed  of 
three  different  substances:  (1)  the  cast-iron  magnet,  (2)  the  wrought- 
iron  bar,  and  (3)  the  two  air-gaps. 

Let  N  —  total  induction  ; 

/i,  A,  and  /a  =  the  average  lengths  of  circuit  in  magnet,  bar,  and 
total  air-gap,  respectively  ; 
Ax,  Ai,  and  A^  =  the  sectional  areas,  respectively  ; 
B;,   B2,  and    83  =  the  magnetic  densities,  respectively  ; 
Ri,  Ra,   and   R3  =  the  reluctances,  respectively  ; 

^1,  ^2,  and  iiz  =  the   permeabilities,    when   the  densities  are  Bi,  89 
and  83,  respectively. 


ELECTRICITY  AND  MAGNETISM.  15G1 

iV 
By   formula  433,  the   ampere-turns   a-t  =  o-Tqo  ^  C*  +  Ra  +  Rs)- 

By  formula  431,  the  reluctance  of  the  circuit  in  the  cast-iron  mag- 

/i                 .       ,         ,       ,     ,        .       .         ,        5  X  3.1416 
net  IS  Ri  =  — ; •.      The   length   of   the  circuit  =  A  = -^ 1- 

6  =  13.854  inches.     The  sectional  ai  ea  =  ^i  =  2  X  1  ==  3  square  inches. 

By  formula  427,  the  density  Bi  =  -r-  =  -^ — =  27,500  lines  of  force 

per  square  inch.     From  Fig,  953,  //  is  about  180,  when  B  =  27,500  in 
cast  iron.     Then  the  reluctance 

R.  =  -^- =  .^^,  =  .03848. 
AiXfh      yxl80 

The  reluctance  of  the  circuit  in  the  wrought-iron  bar  is  Ra  =  — 


^2    X/«2* 

The  length  of  the  circuit  =  4  =  5  +  .25  +  .25  =  5.5  inches.     The  sec- 

tional  area  =A.=  2  X.5  =  1  square  inch.    B^^  ^  =  ^=  55,000  lines 

A2  1 

of  force  per  square  inch.     From  Fig.  953,  //  is  about  1,520  when  B  = 

55,000  in  wrought  iron.     Then,  by  formula  431,  the  reluctance, 

R,  =    ,   ^'        =  :f-4^  =  .00362. 
AiX/^i      1  X  1,520 

Since  one  magnetizing  coil  is  used  for  the  whole  magnetic  circuit, 
the  two  air-gaps  are  added  together,  and  in  the  calculations  a  single 
air-gap  of  double  length,  that  is,  2  X  i  =^  i  inch,  is  considered.     The 

reluctance  of  the  circuit  in  the  air-gap  is  R3  =  —, — ^ .     The  length  of 

the  circuit  =  ^  =  .5  inch.  The  sectional  area  =  ^3  =  3x1  =  2  square 
inches.     In  the  case  of  air,  the  permeability  /^a  =  1. 

/  5 

The  reluctance  is  then  =  —, — =  k- — 5  =  -SS. 

A^Xl^s       2X1 

By  formula  433,  the  necessary  ampere-turns  = 

"i^  000  ^5  000 

^~  X  (.03848  +  .00362  +  .25)  =  ^^^^  x  .2921  =  5,038.05, 

which  means  that  a  magnetizing  force  of  5,033.05  ampere-turns  will 
have  to  circulate  around  the  magnet  arms  to  force  55,000  lines  of  force 
through  the  magnetic  circuit.     Ans. 


RESIDUAL   MAGNETISM. 

241 1.  Residual  magnetism  is  the  magnetism  which 
a  magnetic  substance  retains  after  being  removed  from  a 
magnetic  field.  In  general,  soft  iron  and  annealed  steel  re- 
tain only  a  small  amount  of  magnetism,  and  in  some  cases 


1562  PRINCIPLES  OF 

the  residual  magnetism  is  imperceptible,  A  closed  magnetic 
circuit  of  soft  iron,  that  is,  a  magnetic  circuit  which  consists 
of  soft  iron  throughout  its  entire  length,  will  exhibit  a  large 
amount  of  residual  magnetism  so  long  as  the  circuit  remains 
unbroken.  This  tendency  can  be  shown  by  a  U-shaped 
electromagnet  of  soft  iron,  across  the  two  ends  of  which  is 
placed  a  well-fitted  keeper.  If  the  circuit  is  magnetized  by 
a  current  of  electricity  which  is  suddenly  turned  off,  the 
keeper  will  still  adhere  to  the  ends,  and  may  even  require 
considerable  force  to  detach  it.  But  when  once  it  is  de- 
tached and  the  circuit  broken,  the  keeper  will  not  adhere 
again  without  the  aid  of  the  current. 

Chilled  iron  and  hardened  steel  retain  residual  magnetism 
in  large  quantities.  Artificial  or  permanent  magnets  are 
made  by  placing  a  piece  of  hardened  steel  in  a  dense  mag- 
netic field  or  in  contact  with  another  magnet.  Lodestone  is 
the  result  of  a  natural  residual  magnetism. 


HYSTERESIS. 

2412.  When  the  magnetism  of  an  electromagnet  is 
rapidly  reversed,  that  is,  when  the  direction  of  the  lines  of 
force  is  suddenly  changed  several  times  in  rapid  succession 
by  changing  the  direction  of  the  magnetizing  current,  the 
iron  or  steel  becomes  heated,  and  a  certain  amount  of  energy 
will  be  expended.  This  effect  is  due  to  a  kind  of  internal 
magnetic  friction,  by  reason  of  which  the  rapid  changes  of 
magnetism  cause  the  iron  to  grow  hot.  This  effect  is  called 
hysteresis  (histeree'-sis). 

2413.  The  energy  expended  by  hysteresis  is  furnished 
by  the  force  which  causes  the  change  in  the  magnetism ;  in 
the  case  of  an  electromagnet,  where  the  magnetism  is  re- 
versed by  the  magnetizing  force,  the  energy  is  supplied  by 
the  magnetizing  current. 

The  complete  operation  of  magnetizing  and  demagneti- 
zing an  electromagnet  in  one  direction,  then  magnetizing 
and  demagnetizing  in  the  opposite  direction  by  reversing 
the  magnetizing  current,  is  called  a  cycle  of  magnetism. 


ELECTRICITY  AND  MAGNETISM. 


1563 


One  cycle  is  made  by  two  reversals  of  magnetism.  For  ex- 
ample, reversing  the  magnetism  40  times  in  one  second  will 
make  20  cycles  in  one  second. 

The  loss  of  energy  by  hysteresis  depends  (1)  upon  the 
hardness  and  quality  of  the  magnetic  substance  in  the  core ; 
(2)  upon  the  amount  of  metal  magnetized;  (3)  upon  the 
number  of  cycles  per  second,  and  (4)  upon  the  density  in 
the  substance  when  the  magnetizing  force  is  not  changing. 

2414.  Table  83  gives  the  power  in  watts  expended  by 
hysteresis  in  soft  sheet  iron  when  subjected  to  a  rapid  succes- 
sion of  cycles  of  magnetism  at  different  magnetic  densities. 
The  watts  expended  are  directly  proportional  to  the  number 
of  cycles  per  second  and  to  the  number  of  cubic  inches  of 
iron  magnetized. 

TABLE  83. 


Watts  Expended 

B 

per  Cubic  Inch, 

1  Cycle  per  Sec. 

25,800 

.002320 

32,250 

.002715 

38,700 

.004340 

45,150 

.005320 

51,600 

.006370 

64,500 

.009040 

77,400 

.011920 

90,300 

.015180 

103,200 

.018780      • 

109,650 

.022850 

116,100 

.028150 

Let  zv  =  power  in  watts  expended  per  cubic  inch  per  cycle; 
V  =  volume  in  cubic  inches; 
n  =  cycles  per  second ; 
J>F=  total  watts  expended. 
Then,  W=^w  v  n.  (434.) 


1564 


PRINCIPLES  OF 


Rule. —  To  find  the  pozver  expended  by  hysteresis  in  sheet 
iron  at  a  given  stage  of  magnetization,  multiply  the  watts 
expended  at  that  stage,  as  given  in  Table  83,  or  Fig.  955,  by 

i200O0t 


110000 
100000 
90000 
80000 
70000 
60000 
50000 
40000 


3O000 


20000 


10000 


^ 

y 

/- 

/ 

/ 

/ 

/ 

/ 

) 

1 

/ 

/ 

/ 

/ 

R 

^ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

^005     .010     ,010    ,02O    ,025    .030 

Watts  per  cubic  inch  for  one  cycle. 
Fig.  955. 


,QSS    .040 


the  number  of  cubic  inches  of  iron  in  the  magnet    and  the 
number  of  cycles  per  second. 

The  readings  given  in  Table  83  are  plotted  on  a  sheet  of 
cross-section  paper  in  Fig.  955,  and  the  various  points  are 
connected  by  a  curved   line.     The  ordinates   represent  the 


ELECTRICITY  AND  MAGNETISM.  1565 

different  densities  B,  and  the  abscissas  the  corresponding 
number  of  watts  expended  in  one  cubic  inch  of  iron  for  one 
cycle  per  second.  By  referring  to  the  curve,  all  the  inter- 
mediate values  of  B  and  the  corresponding  watts  expended 
can  be  determined. 

Example. — In  an  electromagnet,  made  with  sheets  of  soft  iron, 
there  are  18  cubic  inches  of  iron.  Find  the  power  in  watts  expended 
when  the  magnetizing  current  is  reversed  70  times  per  second  and  the 
magnetism  reaches  a  density  of  90,000  lines  of  force  per  square  inch. 

Solution. —    70  reversals  are  equivalent  to  35  cycles  =  n.     From 

Fig.  955,  the  watts  expended  per  cubic  inch  for  one  cycle,  at  a  density 

of  90,000,  are  equal  to  .015.     Then,  by  formula  434,  .the  total  power 

expended, 

W  =  .015  X  18  X  35  =  9.45  watts.     Ans. 


LEAKAGE. 

2415.  All  the  lines  of  force  produced  by  the  magneto- 
motive force  can  not  be  confined  along  one  path;  a  certain 
number  in  every  magnetic  circuit  will  stray  froin  the  main 
circuit  and  take  shorter  cuts.  This  tendency  is  called 
xaagnetic  leakage. 

2416.  The  magnetic  leakage  becomes  greater  when  the 
reluctance  along  the  main  circuit  is  not  uniform  at  all  points. 
The  nature  of  magnetic  leakage  may  be  better  understood 
by  remembering  that  air  is  really  a  magnetic  conductor, 
although  its  reluctance  is  much  greater  than  that  of  iron  or 
other  magnetic  substance.  Consequently,  'when  the  re- 
luctance of  the  main  circuit  becomes  large  at  any  point, 
some  of  the  lines  of  force  find  a  shorter  and  easier  path  for 
themselves  through  the  surrounding  air. 

Fig.  956  represents  a  U-shaped  electromagnet  made  of 
iron  with  a  keeper  of  the  same  metal  and  sectional  area. 
By  placing  the  keeper  tightly  against  the  two  ends,  the 
reluctance  becomes  practically  uniform  throughout  the 
entire  magnetic  circuit,  and  there  is  no  perceptible  leakage 
at  any  place.  But  if  the  reluctance  of  the  circuit  is  changed 
by  separating  the  keeper  from  the  ends  of  the  magnet  by  a 
small  air-gap,  as  in   Fig.    957,  the  conditions  are  altered. 


loG6 


PRINCIPLES  OF 


In  the  first  place,  the  total  number  of  lines  of  force  will 
be  reduced  in  all  parts  of  the  circuit,  and,  secondly,  a  cer- 
tain number  of  the  lines  of  force  will  leak  across  from  end 


Fig.  956. 


Fig.  957. 


to  end  of  the  magnet  without  passing"  through  the  keeper. 
The  larger  the  air-gap  between  the  keeper  and  the  magnet, 
the  greater  will  be  the  magnetic  leakage.  An  approximate 
idea  of  the  magnetic   leakage  is  shown  in  Fig.  958,  where 


Fig.  958. 


Fig.  959. 


the  keeper  is  placed  at  a  considerable  distance  from  the  ends 
of  the  magnet,  and  Fig.  959  shows  the  state  of  the  lines  of 
force  when  the  keeper  is  removed  entirely. 


ELECTRICITY  AND  MAGNETISM.  1567 

"  2417.  Magnetic  leakage  may  be  also  defined  as  the 
difference  between  the  number  of  lines  of  force  produced  by 
the  magnetomotive  force  and  the  number  that  are  7iseful  in 
attracting  or  lifting  a  given  weight. 

There  are  no  definite  laws  governing  magnetic  leakage, 
and  it  is  almost  impossible  to  calculate  the  number  of  stray 
lines  of  force  in  any  compound  magnetic  circuit.  After  a 
magnet  is  built,  the  leakage  can  be  determined  with  the 
proper  instruments  and  under  certain  conditions. 

In  general,  if  the  magnetic  circuit  is  composed  of  mag- 
netic substances  whose  permeabilities  are  high  and  there 
are  no  large  air-gaps  to  be  crossed,  the  magnetic  leakage 
will  be  but  a  small  factor. 

2418.  If  the  total  number  of  lines  of  force  produced  by 
the  magnetizing  coils  and  the  useful  number  are  known, 
the  inagnetic  leakage  can  be  expressed  by  a  per  cent,  of  the 
total  number  produced.      Thus, 

Let   /  =  total  number  of  lines  of  force; 
4  =  useful  number  of  lines  of  force; 
/^  =:  stray  lines  of  force; 
/  =  per  cent,  leakage. 

Then, 

4  ==/-/„.         (435.) 

For  example,  assuming  that  60,000  lines  of  force  are  pro- 
duced by  the  magnetizing  coils  of  an  electromagnet,  and 
that  only  42,000  are  useful  in  attracting  an  armature  or 
lifting  a  weight,  then  by  formula  435  the  number  of  stray 
lines  of  force  I,  =  60,000  —  43,000  =  18,000. 

2419.  The  percentage  of   leakage  is  found  from  the 

formula 

100  4  , 

/  =  — J— .  (436.) 

That  is  to  say,  tJie  percentage  of  leakage  is  found  by 
dividing  the  stray  number  of  lines   of  force   by    the   total 


1568  PRINCIPLES 

number  produced  and  multiplying  the  quotient  by  100.      In 

the  above  case 

^       100  X  18,000       ^^  .  .     , 
^=        60,000        -30^^^^kage. 

2420.  To  find  the  total  number  of  lines  of  force  when 
the  percentage  of  leakage  and  the  number  of  useful  lines  of 
force  are  known,  use  the  following  formula: 

^=m~p-      (437.) 

Here  we  divide  the  useful  lines  of  force  by  100  minus  the 
per  cent,  leakage  and  multiply  the  quotient  by  100. 

Example. — Assuming  that  the  magnetic  leakage  in  an  electromag- 
net is  25^  and  that  there  are  75,000  useful  lines  of  force,   how  many 
lines  of  force  are  produced  by  the  magnetizing  coils  ? 
Solution. — By  formula  437,  the  total  lines  of  force 
_  100  X  75,000  _  7,500,000  _ 
^  -      100  -  25      -'        75      ■  -  ■^^"•"^ 
total  lines  of  force  produced  by  the  magnetizing  coils.     Ans. 


EXAMPLES    FOR    PRACTICE. 

2421*  1.  100,000  lines  of  force  are  produced  by  the  magnetizing 
coils  of  an  electromagnet  and  only  40,000  are  useful.  What  is  the  % 
leakage  ?  Ans.  QQ%  leakage. 

2.  In  an  electromagnet  there  are  27,000  stray  lines  of  force  and 
63,000  useful ;  find  the  %  leakage.  Ans.  30j^  leakage. 

3.  The  magnetic  leakage  in  an  electromagnet  is  45^  and  there  are 
110,000  useful  lines  of  force  ;  find  the  total  number  of  lines  produced 
by  the  magnetizing  coils.  Ans.  200,000  lines  of  force. 

4.  If  the  magnetic  leakage  in  an  electromagnet  is  35^  and  there  are 
60,000  lines  of  force  produced  by  the  magnetizing  coils,  how  many  lines 
of  force  are  useful  ?  Ans.  39,000  useful  lines  of  force. 


LIFTING    MAGNETS. 

24:22*  The  lifting  power  or  adhesive  force  of  a  magnet 
is  called  its  tractive  force,  or,  simply,  traction.  The  com- 
mon form  of  electromagnet  for  traction  is  a  stumpy  horse- 
shoe magnet  M  with  two  magnetizing  coils  r,  r,  as  shown  in 
Fig.  960.     The  magnet  is  generally  provided  with  an  arma- 


ELECTRICITY  AND  MAGNETISM. 


1569 


ture  of  soft  iron  a,  which  is  placed  across  the  two  poles.  When 
the  current  is  flow- 
ing in  the  magnet- 
izing coils,  the  full 
tractive  force  of  the 
magnet  is  exerted 
between  the  arma- 
ture and  the  two 
polar  surfaces.  The 
maximum  tractive 
force  is  found  by 
hanging  known 
weights  W  of  any- 
material  upon  the 
armature  in  a  suit- 
able manner  and 
observing  the  heavi- 
est load  it  will  sus- 
tain without  sepa- 
rating from  the 
magnet.     The  total  Fig.  960. 

tractive  force  of  the    magnet    will    be    the    weight    of   the 

armature   plus   the   load 

sustained. 

2423.  Another  eco- 
nomical form  of  electro- 
magnet for  traction  is 
made  in  the  shape  of  a 
'^r  diving-bell,  as  shown  in 
Fig.  961.  This  magnet 
is  iron-clad;  that  is,  the 
magnetizing  coil  is  com- 
pletely surrounded  and 
protected  by  the  return 
magnetic  circuit,  and  re- 
quires only  one  magnet- 
FiG.  961.  izing   coil    to    excite    it. 


1570  PRINCIPLES  OP 

If  the  magnet  proper  M  is  made  in  one  casting,  the  coil  c  is 
wound  independently  in  some  suitable  shape ;  afterwards  it 
is  thoroughly  insulated  by  wrappings  of  cloth,  mica,  or  tape, 
then  placed  around  the  inside  core  of  the  magnet  and  held 
in  position  by  a  ring  of  brass  or  other  non-magnetic  metal  r 
wedged  between  the  core  and  the  outside  shell.  The  con- 
nections to  the  coil  from  an  outside  source  are  inade  to 
leads  (pronounced  leeds)  passing  from  the  coil  up  through 
holes  in  the  top  of  the  magnet.  By  designing  the  magnet 
low  and  large  in  diameter,  the  magnetic  circuit  can  be  made 
exceedingly  short  in  proportion  to  its  sectional  area,  thus 
realizing  one  of  the  conditions  of  an  economical  design. 

2424.  In  determining  the  tractive  force  of  a  magnet, 
let 

A  =  total  area  of  contact  surface ; 

B  =  density  in  lines  of  force  per  square  inch; 

P  =  total  tractive  force  in  pounds. 

That  is,  t/ie  tractive  foi'ce  of  a  magnet  increases  directly 
as  the  total  area  of  the  surface  in  contact  with  the  armature, 
and  as  the  square  of  the  density  of  the  lines  of  force  in  tJie 
magnetic  circuit  where  it  passes  across  that  surface.  For- 
mula 438  is  deduced  from  the  force  exerted  upon  a  unit 
pole  placed  in  a  unit  magnetic  field,  and  assumes  that  the 
distribution  of  the  lines  of  force  is  uniform  throughout  the 
entire  contact  surface.  In  actual  practice  it  is  impossible 
to  obtain  this  result  on  account  of  magnetic  leakage  and 
other  causes.  The  calculated  load  and  the  actual  load 
lifted  will  generally  differ — the  actual  being  somewhat  less 
than  the  calculated,  due  to  the  fact  that  some  of  the  mag- 
netic lines  leak  away  from  the  attracting  surfaces. 

In  all  electromagnets  designed  for  traction  there  will  be 
two  contact  surfaces,  one  at  the  north  pole  of  the  magnet 
and  the  other  at  the  south  pole;  or,  in  other  words,  the 
total  lines  of  force  developed  in  the  magnetic  circuit  are 
used  twice  in  producing  the  traction  of  the  magnet.      If  the 


ELECTRICITY  AND  MAGNETISM.  1571 

two  contact  surfaces  are  symmetrical  and  equal  in  area,  the 
total  tractive  force  of  the  magnet  will  be  twice  the  result 
obtained  by  considering  one  contact  surface  alone;  but  if 
the  contact  surfaces  are  unlike,  the  tractive  force  exerted 
by  each  surface  should  be  calculated  separately,  and  the  two 
results  thus  obtained  added  together. 

2425.  The  most  economical  electromagnet  designed 
for  traction  is  one  that  will  lift  the  greatest  load  in  propor- 
tion to  its  ozvn  iveight.  To  accomplish  this  result,  the  fol- 
lowing facts  must  be  considered: 

The  magnetic  circuit  in  the  magnet  and  keeper  should  be  as 
short  as  possible. 

The  sectio7ial  area  of  the  magnetic  circuit  should  be  uniform 
and  large  in p  -.■oportion  to  the  over-all  dimensions. 

The  iron  or  steel  jcsed  in  the  magnet  and  keeper  should  have 
a  high  permeability. 

The  magnetic  density  of  the  contact  surface  should  be  about 
110  fiOO  lines  of  force  per  square  inch  ^  for,  if  the  magnetism 
is  pusJied  higher  than  this  density,  the  reluctance  of  the  mag- 
netic circuit  zvill  be  increased,  which  increases  the  weight  of 
the  copper  tcsed  in  the  magnetizing  coils. 


CALCULATIOIV  FOR   LIFTING  MAGNET. 

2426.  To  find  the  magnetic  density  at  the  contact 
surface  required  to  produce  a  given  tractive  force  when  the 
area  of  the  contact  surface  is  known : 

Let  A  =  area  of  contact  surface  in  square  inches  ; 
P  =  tractive  force  in  pounds ; 

B  =  magnetic    density    of  lines   of   force    at   contact 
surface. 

Then.  B  =  8,493 1/^.  (439.) 

Rule. — In  an  electromagnet  the  density  of  lines  of  force  at 
the  contact  surface  is  equal  to  8,Jf93  times  the  square  root 
of  tJie  tractive  force  in  pounds  divided  by  the  area  in  square 
inches. 


1572  PRINCIPLES  OF 

2427.  To  find  the  total  number  of  lines  of  force  in  the 
magnetic  circuit  when  the  tractive  force  and  the  magnetic 
density  at  the  contact  surface  are  known: 

Let  N  —  the   induction,  or   the   total  number  of  lines  of 
force. 

Then,  i\^=  72,134,000-^.  (440.) 

Rule. —  The  total  number  of  lines  of  force  in  an  electro- 
magnet is  found  by  dividing  the  tractive  force  in  pounds  by 
the  magnetic  density  at  the  contact  surface  and  multiplying 
the  quotient  by  72,13Jt.,000. 

2428.  To  find  the  tractive  force  in  pounds  per  square 
inch  when  the  area  of  the  contact  surface  and  the  total 
number  of  lines  of  force  are  known: 

Let  p  =  tractive  force  in  pounds  per  square  inch. 

JSf 

Rule. —  The  tractive  force  of  an  electromag7tet  in  pounds 
per  square  inch  is  equal  to  the  square  of  tJie  number  of  lines 
of  force  divided  by  72,13 Jf.,000  times  tJie  square  of  the  area 
of  contact  surface  in  square  inches, 

2429.  To  find  the  tractive  force  in  pounds  per  square 
inch  when  the  density  at  the  contact  surface  is  known: 

^  ^  72,134,000*  (442.) 

Rule. —  The  tractive  force  of  an  electromagnet  in  pounds 
per  square  inch  is  equal  to  the  square  of  the  magnetic  density 
at  the  contact  surface  divided  by  72,13Jf.,000. 

2430.  To  find  the  area  of  the  contact  surface  when  the 
total  number  of  lines  of  force  and  the  tractive  force  are 
known : 

^  "^  72,134, 000  :P*  (443.) 


ELECTRICITY  AND  MAGNETISM.  1573 

Rule. —  The  total  area  of  eontact  surface  of  an  electro- 
magnet is  found  by  dividing  the  square  of  the  total  number  of 
lines  of  force  by  72,13^,000  times  the  tractive  force  in  pounds. 

2431.  To  find  the  number  of  ampere-turns  required  to 
energize  a  magnet  for  a  given  traction  when  the  permeability 
of  the  iron  or  steel  use.d  is  known  and  the  dimensions  of  the 
armature  and  magnet  have  been  established: 

Let  P=  tractive  force  of  one  contact   surface;  then, 
2  P  is  the  total  tractive  force  of  the  magnet ; 
/j  and  /j  =  the  lengths  of  the  magnetic  circuit  in  magnet 
and  armature,  respectively; 
A^  and  A^  =  sectional  areas  of  magnetic  circuit  in  magnet 
and  armature,  respectively; 
^,  and//^  =  permeabilities  of  the  iron  or  steel  used  in  the 
magnet  and  armature,  respectively; 
B  =  magnetic  density  at  contact  surface. 
Then,  the  ampere-turns 

a-,  =  82,598,370  X  ^X  {^^^^  +  ^).  (444.) 

Rule. — In  the  case  of  an  electromagnet  htte^ided  to  develop 
a  given  tractive  power,  the  ampere-turns  are  equal  to  the  tract- 
ive force  of  one  contact  surface  multiplied  by  the  reluctance 
of  the  circuit  and  by  22,598,370^  and  divided  by  the  magnetic 
density  at  the  contact  stirface. 

2432.  To  find  the  ampere-turns  required  to  energize  a 
magnet  for  a  given  tractive  force  when  the  armature  and 
magnet  are  made  of  the  same  quality  of  iron  or  steel  and 
the  sectional  area  of  the  magnetic  circuit  is  the  same  in  the 
armature,  magnet,  and  contact  surfaces: 

Let  /=  total  length  of  magnetic  circuit  in  inches; 

7^=  tractive  force  at  one  surface; 

\i,  z=  permeability  of  iron  or  steel  used; 

A  =  cross-sectional  area  of  magnetic  circuit; 

JV=  total  number  of   lines  of  force  in  the  magnetic 

circuit. 

/         /P 
The  ampere-turns  necessary,  a-t  =  2,661  X  —X  f  -j.   (445.) 


1574  PRINCIPLES  OF 

Rule. —  7^0  determine  the  ampere -turns  for  an  electromagnet 
of  uniform  sectional  area  and  material  wkeit  the  tractive 
force  at  one  surface  is  given  ^  find  the  square  root  of  the  tractive 
force  divided  by  the  area,  multiply  this  value  by  2,661  times 
the  length  of  circuit  in  inches  and  divide  by  the  permeability. 

As  showing  the  relation  between  formulas  439  and  445 » 
the  latter  may  be  written : 


5,493'/^ 


"-^=      3.192       X]I-3392>^?  (446.) 

2433.  In  designing  an  electromagnet  for  a  certain 
tractive  force,  several  assumptions  have  to  be  made  in  the 
beginning.  The  first  assumption  is  the  magnetic  density  in 
the  armature,  magnet,  and  contact  surface.  If  wrought 
iron,  cast  steel,  or  soft  annealed  sheet  iron  is  used,  the  density 
in  the  armature  and  magnet  should  be  between  100,000 
and  120,000  lines  of  force  per  square  inch.  If,  however,  the 
metal  is  gray  cast  iron,  the  density  should  be  between 
50,000  and  70,000  lines  of  force  per  square  inch.  As  already 
stated,  the  density  of  the  contact  surface  in  any  coil  should 
be  about  110,000  lines  offeree  per  square  inch.  If  the  mag- 
net is  made  of  cast  iron  in  which  the  density  is  low,  the 
edges  of  the  pole-pieces  should  be  chamfered  off  to  increase 
the  density  of  the  contact  surface.  This  chamfering  will 
slightly  increase  the  reluctance  of  the  magnetic  circuit  at 
that  point,  but  the  amount  will  be  small  and  can  be  neglect- 
ed. The  next  assumptions  are  the  over-all  dimensions  of 
the  magnet.  The  relation  between  the  tractive  force  for 
which  the  magnet  is  to  be  designed  and  the  magnetic 
densities  determines  the  sectional  areas  of  the  armature  and 
magnet,  but  does  not  give  any  information  regarding  the 
over-all  dimensions.  Several  trials  may  be  necessary  to  de- 
termine the  most  economical  dimensions.  In  the  first  trial, 
ample  space  should  be  left  for  the  magnetizing  coils,  and  if 
this  space  is  found  to  be  too  small  or  larger  than  necessary, 
the  over-all  dimensions  should  be  changed  and  the  magnet 
recalculated. 


ELECTRICITY  AND  MAGNETISM.  1575 

Example. — Design  an  electromagnet  for  a  maximum  tractive  force 
of  672  pounds. 

Solution. — From  formula  4-43  the  tractive  force  in  pounds  per 
square  inch  p  =  i-.:,    oa  (\(\c\  •     Using  a  density  of  110,000  lines  of  force  at 

the  contact  surface  gives  p  =  ., ,  ..',  ,„„.   =  167.74,  or  about  168  pounds 
*  -^       72,184,000  '■ 

per  square  inch.  The  total  tractive  force  divided  by  the  tractive  force 
per  square  inch  gives  the  total  area  of  the  contact  surfaces.  There- 
fore, -^11  =  4  square  inches  for  the  area  of  the  two  contact  surfaces,  or 
2  square  inches  for  the  area  of  one  contact  surface.  The  total  lines  of 
force  in  the  circuit  are  110,000  X  3  =  220,000. 

In  the  first  trial,  imagine  a  bar  of  wrought  iron  8  in,  long,  2  in.  wide, 
and  1  in.  thick,  bent  in  the  direction  of  its  least  dimension  into  the 
form  of  a  horseshoe  with  straight  sides,  so  that  the  distance  between 
the  centers  of  the  poles  is  3  in.  The  armature  maybe  a  bar  of  wrought 
iron  4  in.  long,  2  in.  wide,  and  1  in.  thick.  The  sectional  area  of  the 
magnetic  circuit  is  2  square  inches  in  magnet,  armature,  and  contact 
surface,  and  the  density  is  110,000  lines  of  force  per  square  inch.  From 
Table  82,  when  B  =  110,000  the  permeability  in  wrought  iron  is  106.3. 
The  mean  length  of  the  magnetic  circuit  in  the  magnet  is  8  in.,  and  in 
the  armature  it  is  3  +  -J-  +  -J-  =  4  in. ;  hence,  the  total  length  /  is  8  +  4  = 

12  in.    By  formula  445,  the  ampere-turns  «-/  =  2:661  v  .  y  a/'-—  — 

106.3  ^T      2    ~ 
12 
2,661  Xjwr^jX  12.961  =  3,893.42,  or  about  3,893  ampere-turns  required 

to  magnetize  the  magnetic  circuit  under  these  conditions. 

Assuming  the  current  to  be  10  amperes,  then  3,893  -=-10  =  389.3,  or 
say  389  turns  of  a  conductor  to  be  wound  around  the  magnet.  A  cop- 
per wire  covered  with  two  layers  of  cotton  thread  can  be  used  for  the 
conductor.  A  size  of  wire  must  be  used  which  will  not  heat  excessively 
when  a  current  of  10  amperes  is  flowing  through  it.  From  experiment, 
it  is  found  that  a  copper  wire. 091  in.  in  diameter  will  carry  10  amperes 
with  safety.  After  the  wire  has  been  covered  with  two  layers  of  cot- 
ton, the  diameter  will  be  about  .1  in.  The  wire  should  be  wound  in 
tAVo  coils,  one  on  each  pole  of  the  magnet.  If  each  coil  is  wound  in 
layers  extending  2  in.  from  the  polar  surfaces,  there  will  be  2  -r-  .1  = 
20  turns  of  wire  lying  side  by  side,  or  20  turns  in  each  layer  in  each 
coil.  The  total  number  of  turns  in  each  coil  should  be  -^^  =  194.5,  or 
say  195. 

The  number  of  turns  divided  by  the  turns  in  one  layer  will  give  the 
number  of  layers;  therefore,  ^^^-  =  9.75  layers  in  each  coil.  The  maxi- 
mum depth  of  wire  will  be  10  layers  or  1  in.  on  each  coil,  which  exactly 
fills  up  the  space  between  the  two  poles  after  both  coils  have  been 
wound.  It  is  better  practice,  however,  to  design  the  magnet  with 
some  space  between  the  two  coils ;  in  the  preceding  example  a  space  of 
from  i  inch  to  |  inch  might  have  been  allowed  between  the  two  coils. 


1576 


PRINCIPLES  OP 


MAGNETS  FOR  ATTRACTION. 


SHORT-RANGE  MAGNETS. 

2434.     Electromagnets   designed   for  attracting    theii 
armatures  through  a  distance  can  be  divided  into  two  sub- 
classes,   namely,    short 


2Si6ilong  r^/z^^" magnets. 
Short-range  mag- 
nets are  used  in  places 
where  the  armature  is 
required  to  move  rapid- 
ly through  a  short  dis- 
tance, exerting  compar- 
FiG.  9G2.  atively  little  force ;  as, 

for  example,  in  telegraph  apparatus,  electric  bells,  arc 
lights,  etc.  Such  magnets  are  usually  of  the  horseshoe 
type,  as  shown  in  Fig.  9G2,  which  represents  an  electro- 
magnet for  a  telegra-ph  relay.  In  this  particular  mag- 
net the  cores  are  made  of  two  round  bars  of  soft  iron 
M^  f  in.  in  diameter  and  2  in.  long.  The  cores  are  screwed 
into  a  yoke  of  soft  iron  b,  f  in.  wide  by  \  in.  thick  and  2  in. 
long.  The  magnetizing  coils  are  wound  over  vulcanized 
rubber  bobbins  or  spools,  and  contain,  all  told,  about  8,500 
convolutions,  or  turns,  of  insulated  copper  wire  .009  in.  in 
diameter.  The  total  resistance  of  the  wire  in  the  two  mag- 
netizing coils  is  about  150  ohms.  A  vulcanized  rubber  shell 
or  cover  c  is  slipped  over  each 
coil  when  wound,  to  protect  it 
from  dust  and  bruises. 


2435.  Fig.  963  represents 
another  form  of  magnet  used 
for  rapid  vibrations  of  the  ar- 
mature. The  cheapness  of 
winding  only  one  coil  instead 
of  two  and  its  simplicity  of 
construction  recommend  it  for 
a  large  variety  of  practical  uses. 


Fig.  963. 


The  principal  disadvan- 


ELECTRICITY  AND  MAGNETISM. 


1577 


tage  is  the  large  amount  of  magnetic  leakage  caused  by  an 
unbalanced  magnetic  field.  There  is  a  large  variety  of  short- 
range  electromagnets  adapted  to  special  uses,  -but  all  the 
various  types  are  modifications  of  the  same  general  principle. 
The  magnitude  of  the  force  which  short-range  electro- 
magnets are  usually  required  to  exert  is  comparatively 
small ;  in  most  cases  the  armature  moves  only  a  fraction  of 
an  inch  against  the  tension  of  a  light  helical  spring.  Conse- 
quently, it  is  unnecessary  to  calculate  the  magnetic  circuit 
and  the  force  of  attraction.  The  size  and  amount  of  wire  to 
be  used  for  the  magnetizing  coils  depend  upon  the  local  con- 
ditions, and  the  most  satisfactory  results  are  obtained  by 
experimental  trials  in  each  particular  case. 


LOIVG-RANGE  MAGNEXS. 

2436.  The  most  economical  form  of  long-range  mag- 
nets is  the  coil-and-plunger  magnet ;  that  is,  a  magnet 
in  which  a  part  or  the  whole  of  the  armature  moves  inside 
the  magnetizing  coils.  The  simplest,  although  the  most  in- 
efficient, type  of  such  magnets  is  a  straight  bar  of  iron  mov- 
ing freely  into  one  magnetizing  coil  or  solenoid.  The  bar 
will  always  be  attracted  towards  the  center  of  the  solenoid, 
with  its  neutral  line  coincidine  with  that  of  the  solenoid. 


The  range  of  action  is  long,  but  the  force  exerted  is  com 
paratively  weak. 

Fig.  964  represents  an  effective  type  of  coil-and-plunger 


1578 


PRINCIPLES  OF 


magnet,  and  one  capable  of  exerting  heavy  pulls  through 
long  ranges.  The  magnetic  circuit  is  divided  at  about  the 
center  of  the  coils  c,  c,  and  half  of  each  core  is  attached  to 
the  armature  a.  The  advantage  thus  gained  consists  in 
causing  the  greatest  reluctance  to  take  place  where  the  mag- 
netizing force  is  the  strongest,  and,  hence,  the  tendency  to 
magnetic  leakage  is  reduced.  A  coil-and-plunger  magnet  of 
this  type  weighing  about  65  pounds  will  give  an  initial  pull 
of  approximately  50  pounds  when  the  air-gap  between  the 
cores  of  the  armature  and  the  cores  of  the  yoke  is  3  inches. 
As  soon,  however,  as  the  armature  starts  to  move  into  the 
coils,  the  reluctance  of  the  magnetic  circuit  and  the  mag- 
netic leakage  are  reduced ;  consequently,  the  density  of  the 
magnetic  field  increases,  which  in  turn  increases  the  attract- 
ive force.  If  the  magnetizing  force  remains  unchanged, 
the  attractive  force  when  the  armature  has  moved  through 
only  part  of  the  distance  will  be  several  times  the  initial 
attractive  force. 


2437.  A  combination  of  the  coil-and-plunger  and  iron- 
clad types  with  one  magnetizing  coil  gives  an  efficient  mag- 
net for  powerful  pulls  over  short 
ranges.  The  inside  core  in,  in- 
stead of  protruding  above  the 
top  of  the  magnetizing  coil  as 
in  ordinary  short-ranged  iron- 
clads, rises  to  only  about  half 
the  height  of  the  coil,  as  shown 
in  Fig.  905.  The  other  half  of 
the  core  n  is  attached  to  the 
armature  a,  and  moves  inside 

the  magnetizing  coil  c.       This 
Fig.  9G5.  .  ,     .  ,  , 

IS  wound   m  a  metal  spool  or 

bobbin,  which  is  rigid  enough  to  serve  as  a  guide  for  the 

armature.     The  range  of  action  is  limited  on  account  of  the 

enormous  magnetic  leakage  taking  place  across  the  top  of 

the  coil  when  the  air-gap  becomes  large. 


ELECTRICITY  AND  MAGNETISM. 


1579 


ELECTROMAGNETIC  IIVDUCTION. 

2438.  It  has  been  shown  that  a  magnet  and  a  con- 
ductor carrying  a  current  of  electricity  exert  a  mutual  force 
upon  each  other  ;  or,  in  other  words,  each  tends  to  produce 
motion  in  the  other.  In  general,  when  a  conductor  carry- 
ing a  current  of  electricity  is  placed  in  a  magnetic  field,  the 
conductor  will  tend  to  move  in  a  definite  direction  and  with 
a  certain  force,  depending  upon  the  strength  and  direction  of 
the  current  and  upon  the  direction  and  density  of  the  lines 
of  force. 


Direction 
gj  motion- 


2439.     To  determine  the  direction  of  motion  of 
a   conductor   carrying   a    cur- 
rent      of       electricity        ^vlien 
placed  in  a  magnetic  field  : 

Rule. — Place  thumb,  forefinger, 
and  middle  finger  of  the  left  hand 
each  at  right  angles  to  the  other 
two,  as  shozvn  in  Fig.  966 ;  if  the 
forefinger  shozvs    the  direction    of  fig.  966. 

the  lines  of  force  and  the  viiddle  finger  sJiozvs  t lie  direction  of 
the  current,  then  the  thumb  will  show  the  direction  of  motion 
given  to  the  conductor. 

The  direction  of  motion  produced  in  the  conductor  can 

also  be    graphically    shown. 

The  diagram.  Fig.  967,  indi- 
cates a  cross-section  of  a  mag- 
netic field;  the  dots  repre- 
sent an  end  view  of  the  lines 
of  force,  and  the  heavy  line  a 
conductor  conveying  a  cur- 
rent of  electricity.  If  the 
direction  of  the  lines  of  force 
is  dowmvards,  that  is,  pier- 
y  cing  the  paper,  and  if  the  cur- 

J  rent  flows  in  the  direction  in- 

FiG.  967.  dicated  by  the  arrow-heads, 


C, 

liBi 

^ 

^B 

^■^  K 

7^ 

1580 


PRINCIPLES  OP 


then   the  conductor  will  be  moved  bodily  to  the  right^  as 
indicated  by  the  two  arrows. 

2440.     This  action  is  also  true  of  an  electric  arc  passing 
through  a  magnetic  field,   that  is,  a  current  of  electricity 
passing  or  jumping  in  the  form  of  a  con- 
tinuous   spark    between    two    electrodes 
across  an  air-space  which  is  traversed  by 
lines  of  force,  as  indicated   in   Fig.   968. 
^IH  The  arc  or  spark  will  be  impelled  to  one 
5^5^  ^ll  side  in  the  same  direction  as  the  conductor 
in  the   previous   case.      If  the   electrodes 
remain  in  a  fixed  position  relative  to  the 

Vj  magnetic  field,  the  arc  will  be  blown  out ; 
^             that  is,  the  spark  will  be  extinguished  and 

Fig.  968.  ^j^Q  current  will  cease  to  flow  in  the  cir- 

cuit. In  both  cases  the  motion  is  caused  by  the  mutual 
action  of  the  lines  of  force  in  the  magnetic  field  and  those 
produced  by  the  current  itself,  as  shown  in  Fig.  969, 
where  the  current  is  assumed  to  be  flowing  downwards. 
The  lines  of  force  in  the  magnetic  field  tend  to  coincide  in 
direction  with  those  around  the  current,  and  in  doing  so 
they  exert  a  crowding  effect  on  the  current,  which,  in 
the  first  case,  produces 
motion  in  the  conductor, 
and  in  the  second  a  ten- 
sion upon  the  arc. 


N 


S 


2441.     The    converse  Fig.  969. 

of  this  effect  is  also  true,  namely,  when  a  conductor  forming 
a  closed  circuit  is  moved  across  a  magnetic  field  at  right 
angles  to  the  lines  of  force^  a  ciirrent  is  induced  in  the  con- 
ductor. 

This  statement  will  be  better  understood  by  comparing 
the  action  in  Fig.  967  with  that  in  Fig.  970.  In  the  former 
case,  when  a  current  is  flowing  in  the  direction  indicated 
by  the  arrow-head  the  conductor  will  move  bodily  to 
the   right.     In  Fig.   970,  however,   when  the  conductor   is 


ELECTRICITY  AND  MAGNETISM. 


1581 


Wz 


M 


moved  to  the  right  by  some   exterior  means  a  current  is 
induced  in  it  which  tends  to  flow  in  an  opposite  direction 

to    the    current    which   pro-     ^ >^ 

duces   the    same    motion    in 
the  former  case. 

This  generation  of  current 
may  be  explained  by  saying 
that  the  motion  of  the  con- 
ductor across  the  lines  of 
force  from  the  magnet  sets 
up  an  electromotive  force  in 
the  conductor,  which,  when 
the  circuit  is  completed, 
causes    a    current    to    flow.     ^  ■■■.    ^ 

The  direction  of  the  current  ^' i°-  9™- 

induced  in  the  conductor  will  be  at  right  angles  to  the  lines 
of  force  and  to  the  direction  of  motion  of  the  conductor. 

2442.  To  determine  the  direction  of  induced 
currents : 

Rule. — Place  thumb,  forefinger,  and  middle  finger  of  the 
right  hand  each  at  right  angles  to  the  other  tzvo  ;  if  the  fore- 
finger shozi's   the    direction   of  the   lines   of  force  and  the 

thumb  shozus  the  direction  of  motion 
of  conductor,  the  middle  finger  will 
shoiv  the  direction  of  the  induced 
ctirrent.      (See  Fig.  971.) 


2443.     The  positive  end  of  a 

conductor  in  which  a  current  is  gen- 
erated by  moving  across  a  magnetic 
Fig.  971,  field  is  that  end  towards  which   the 

current  tends  to  flow ;  the  negative  end  is  that  from  which 

the  current  tends  to  flow. 

2444.  An  electric  current  will  be  induced  in  a  coiled 
conductor  when  a  pole  of  a  magnet  is  suddenly  inserted  into 
the  coil.  The  current  will  be  continuous  so  long  as  there  is 
a  change  in  the  member  of  lines  of  force  passing  through  the 


1583 


PRINCIPLES  OF 


coil,  but  the  current  will  cease  to  flow  when  the  number  of 
lines  of  force  becomes  constant,  that  is,  when  the  lines  of 
force  inside  the  coil  do  not  increase  or  diminish  in  number. 

In  reality,  currents  produced  in  a  conductor  cutting  lines 
of  force  and  currents  induced  in  a  coiled  conductor  by  a 
change  in  the  number  of  lines  of  force  which  pass  through 
the  coil  are  due  to  the  same  motion,  for  every  conductor 
carrying  a  current  of  electricity  forms  a  closed  coil,  and  every 
line  of  force  is  a  complete  magnetic  circuit  by  itself.  Con- 
sequently, when  any  part  of  a  closed  coil  is  cutting  lines  of 
force,  the  lines  of  force  are  passing  through  the  coil  in  a 
definite  direction,  and  changing  at  the  same  rate  as  the 
cutting. 

In  calculations,  however,  it  is  more  convenient  to  make  a 
distinction  between  the  two  cases,  and  to  consider  that  the 
current  or,  more  strictly,  the  E.  M.  F.,  in  the  first  case  is 
generated  by  a  conductor  of  a  certain  length  cutting  the 
lines  of  force  at  right  angles;  while,  in  the  second  case,  the 
current  in  a  closed  coil  is  induced  by  a  change  in  the  number 
of  lines  of  force  passing  through  the  coil. 

2445.  The  action  of  induced  currents  can  be  shown  by 
a  closed  coil  of  any  conducting  material  moving  in  a  mag- 


FlG.  972. 


netic  field.  If  it  is  moved  in  a  uniform  field  along  the  lines 
of  force,  as  in  Fig.  972,  so  that  only  the  same  number  of 
lines  of  force  pass  through  it,  no  current  will  be  generated. 
Or,  if  the  coil  be  moved  across  the  lines  of  force  in  a  uniform 


ELECTRICITY  AND  MAGNETISM. 


1583 


field,  Fig.  973,  as  many  lines  of  force  are  left  behind  as  are 
gained  in  advancing,  and  there  will  be  no  current  generated 
in  the  coil.     Rotating  the  coil  on  a  central  axis,  like  the  rim 


FIG.  973. 

of  a  pulley,  will  not  generate  a  current,  because  there  is  no 
change  in  the  number  of  lines  of  force  passing  through  the 

loop. 

But  if,   as  in  Fig.    974,    the   coil  be  tilted  in  its  motion 
across  the  uniform  field,  or  rotated  around  on  any  axis  in 


N 


Fig.  974. 


its  own-  plane,  then  the  number  of  lines  of  force  that  pass 
through  it  will  be  altered  and  a  current  will  be  developed. 
Where  the  magnetic  field  is  not  uniform,  the  removal  of  the 
coil  bodily  from  a  place  where  the  lines  of  force  are  dense  to 
where  they  are  less  dense,  as  from  position  1  to  position  2 


1584 


PRINCIPLES  OF 


in  Fig.  975,  will  cause  the  generation  of  a  current  in  the 
coil  ;  or  if  the  coil  is  moved  to  a  place  where  the  direction 


Fig.  975. 
of  the  lines  of  force  is  reversed,  the  effect  will  be  the  same. 

2446.  To  determine  tlie  direction  of  induced 
currents  in  a  closed  coil : 

Rule. — If  the  effect  of  the  movemejit  is  to  diminish  thi 
number  of  lines  of  force  that  pass  through  the  coil,  the  cur- 
rent will  flow  around  in  the  conductor  in  the  direction  of  the 
hands  of  a  watch  as  viewed  by  a  person  looking  along  the 
^nagnetic  field  in  the  direction  of  the  lines  of  force ;  but  ij 
the  effect  is  to  increase  the  niunber  of  lines  of  force  that  pass 
through  the  coil,  the  current  will  flow  aroimd  in  the  opposite 
direction. 

2447.  In  the  explanations  just  given,  it  was  stated 
that  currents  are  generated  by  moving  the  conductor  in  a 
magnetic  field.  It  must  be  remembered,  however,  as 
shown  in  the  beginning,  that  a  current  is  merely  the 
equalization  of  a  difference  of  potential.  Strictly  speaking, 
therefore,  it  is  not  actually  a  current,  but  electromotive 
force,  that  is  developed  by  induction  in  the  moving  con- 
ductor ;  for,  on  opening  the  circuit,  the  electromotive  force 
will  still  exist,  but  no  current  can  flow.  The  word  current 
is  used  merely  to  avoid  complication. 


ELECTRICITY  AND  MAGNETISM, 


1585 


Fig.  976. 


EXPERIMENTS  W^ITH  ELECTRICAL  APPARATUS. 

2448.  (Art.  2439.)  Take  a  piece  of  wire  about 
12  inches  long  ;  about  an  inch  each  side  of  the  center  make 
a  right-angle  bend  ;  bare  the  ends  of  the  wire  and  bend 
about  an  inch  of  each  end  into  a  loop.  This  will  make  a  sort 
of  trapeze  of  wire,  as 
shown  at  .-i  A,  Fig.  976. 
Bare  the  ends  of  two 
wires  leading  from  the 
battery  (via  the  revers- 
ing switch),  scrape  them 
bright  to  ensure  good 
contact,  and  support 
them  in  the  same  line 
about  2  inches  apart, 
so  that  the  bent  wire  may  hang  from  them,  as  shown 
in  the  figure,  where  vS"  and  vS  represent  the  supports  of  the 
wires. 

Now,  hold-  the  horseshoe  magnet  M,  Fig.  976,  in  such  a 
position  that  the  bent  wire  may  swing  freely  between  its 
poles,  and  with  the  switch  complete  the  circuit,  [a)  What 
happens  ?  {b^  Reverse  the  current  through  the  hanging 
loop  ;  what  happens  ?  (r)  How  can  you  foretell  which  way 
the  wire  will  swing  ? 

(Art.  2439.)  Replace  the  bent  wire  in  the  above  ex- 
periment with  a  wire  bent  into  a  coil  of  about  three  turns, 
large  enough  to  slip  freely  over  one  pole  of  the  magnet,  and 
suspend  this  coil,  as  before.  Repeat  the  first  two  experi- 
ments, using  this  coil  instead  of  the  wire  trapeze.  Are  the 
effects  noted  above  altered  any  ?     Why  ? 


DETERMINATION    OF    E.    M.    F. 

2449.  The  electromotive  force  generated  in  a  con- 
ductor cutting  lines  of  force  at  right  angles  is  proportional 
to  the  rate  of  cutting.  The  rate  of  cutting  is  found  by 
dividing  the  number  of  lines  cut  by  the  time  taken  to  cut 
them. 


1586  PRINCIPLES  OF 

One  absolute  unit  of  potential  !•&  generated  in  a  conductor 
when  it  is  cutting  lines  of  force  at  the  rate  of  one  line  of 
force  per  second. 

By  definition,  one  volt  is  equal  to  100,000,000  (10^)  absolute 
units  (see  Art.  2303)  ;  consequently,  in  order  to  generate 
an  electromotive  force  of  one  volt,  the  rate  of  ciitting  must 
be  10^  lines  of  force  per  second.  This  can  also  be  expressed 
algebraically. 

Let  E  =  the  electromotive  force  in  volts  ; 

N  =  the  total  number  of  lines  of  force  cut  by  the  con- 
ductor ; 
t  =  time  in  seconds  taken  to  cut  the  lines  of  force. 

Then,  £  =  Ji^r  (447.) 

That  is,  t/ie  electromotive  force  in  volts  generated  in  a  mov- 
ing conductor  is  found  by  dividing  the  total  number  of  lines 
of  force  cut  by  the  conductor  by  the  time  taken  and  by 
100,000,000. 

If  the  total  number  of  lines  of  force  remains  unchanged, 
the  electromotive  force  developed  is  the  same,  whether  the 
lines  of  force  proceed  from  a  permanent  magnet  or  electro- 
magnet. 

2450.  According  to  Ohni's  lazv,  the  current  obtained 
from  conductors  cutting  lines  of  force,  is  equal  to  the  quo- 
tient arising  from  dividing  the  total  electromotive  force 
generated  by  the  total  resistance  of  the  circuit  through 
which  the  current  passes.  In  general,  the  total  resistance 
is  the  resistance  of  the  conductor  cutting  the  lines  of  force, 
or  the  resistance  of  the  internal  circuit,  plus  the  resistance 
of  any  conductor  or  conductors  which  complete  the  external 
circuit.  If  E  represents  the  total  electromotive  force  in 
volts,  r^  and  r^  the  resistance  in  ohms  of  the  internal  and 
external  circuits,  respectively,  and  C  the  current  in  amperes, 

E 
then  C  =  ■ ; . 

It  will  be  seen  from  the  above  expression  that  a  large  or 
small   induced   current   can   be  obtained   from   conductors 


ELECTRICITY  AND  MAGNETISM.  1587 

cutting  lines  of  force  by  simply  changing  the  combined 
resistance  of  the  internal  and  external  circuits.  There  is, 
however,  a  maximum  limit  to  the  amount  of  current 
obtained  in  this  manner.  The  lines  of  force  which  are  pro- 
duced around  the  conductor  by  the  current  itself  will  always 
act  in  opposition  to  the  lines  of  force  producing  the  electro- 
motive force,  and  will  tend  to  distort  or  crowd  them  away 
from  their  original  direction.  The  number  of  lines  of  force 
produced  around  the  conductor  by  the  current  is  directly 
proportional  to  the  strength  of  the  current  ;  and,  conse- 
quently, as  the  current  becomes  larger  and  larger,  the  lines 
of  force  cutting  the  conductor  become  more  and  more  dis- 
torted and  crowded  away  from  their  original  direction,  until 
the  conductor  no  longer  cuts  all  the  lines  of  force,  and,  there- 
fore, the  electromotive  force  generated  becomes  smaller. 
A  general  rule  to  get  rid  of  this  effect  is  to  make  the  density 
of  the  magnetic  field  large  in  proportion  to  the  current. 


PRODUCTION    OP    INDUCED    E.    M.    F. 

2451.  There  are  three  ways  of  producing  an  electro- 
motive force  by  induction  in  a  coiled  conductor,  namely,  by 
electromagnetic  induction^  by  self-induction,  and  by  mutual 
induction. 

2452.  In  electromagnetic  induction  the  change 
in  the  number  of  lines  of  force  which  pass  through  the  coil 
is  due  to  some  relative  motion  between  the  coil  and  the 
magnetic  field;  as,  for  example,  by  thrusting  a  magnet  pole 
into  the  coil,  or  by  taking  the  magnet  out  from  the  coil,  or 
by  suddenly  turning  the  coil  in  a  magnetic  field. 

2453.  In  self-induction  the  change  in  the  number 
of  lines  of  force  is  caused  by  sudden  changes  in  a  current 
which  is  flowing  through  the  conductor  itself  and  supplied 
from  some  exterior  source.  If  this  exterior  current  is  sud- 
denly increased,  it  will  produce  a  change  in  the  number  of 
lines  of  force ;  the  change  in  turn  induces  an  electromotive 
force  in  the  conductor  which  opposes  the  exterior  current 
in  the  coil  and  tends  to  keep  it  from  rising.     The  exterior 


1588 


PRINCIPLES  OF 


current  will  eventually  reach  its  maximum  strength  in  the 
coil,  but  its  progress  will  be  greatly  retarded  by  the  induced 
electromotive  force.  If,  on  the  contrary,  the  exterior  cur- 
rent is  suddenly  allowed  to  decrease,  it  will  produce  a  change 
in  the  lines  of  force;  this  change  induces  an  electromotive 
force  in  the  coil  which  acts  in  the  same  direction  as  that  of 
the  exterior  current,  and  tends  to  keep  it  from  decreasing. 
As  in  the  previous  case,  the  exterior  current  will  eventually 
decrease  to  its  minimum  strength,  but  it  will  fall  gradually, 
and  a  portion  of  a  second  will  elapse  before  it  becomes  con- 
stant. In  fact,  the  current  flowing  through  a  coiled  con- 
ductor acts  as  if  possessing  inertia ;  any  sudden  change  in 
the  strength  of  the  current  will  produce  a  corresponding 
electromotive  force  which  will  tend  to  oppose  that  change 
and  keep  the  current  in  its  original  strength. 


r^mH 


24:54:,  In  mutual  induction,  two  separate  coiled  con- 
ductors, one  carrying  a  current  of   electricity,   are  placed 

near  each  other,  so  that  the 

magnetic     circuit    produced 

by  one  will   be   enclosed  by 

the  other,  as  shown  in  Fig. 

977,  in  which  the  current  is 

Fig.  977.  flowing  around  coil  P. 

The  coil  (P)  around  which  the  current  is  flowing  is  called 

the   primary  or  exciting    coil ;    the    other    (5)    is    the 

secondary  coil. 

Any  change  in  the  strength  of  the  current  flowing  around 
\)s\Q  primary  coil  will  produce  a  corresponding  change  in  the 
lines  of  force  in  the  magnetic  circuit,  and,  consequently,  an 
electromotive  force  will  be  induced  in  the  secondary  coil.  If 
the  current  in  the  primary  coil  is  increasing^  the  electro- 
motive force  induced  in  the  secondary  coil  will  cause  a  cur- 
rent to  flow  around  in  the  opposite  direction  to  the  current 
in  the  primary  coil.  If  the  current  in  the  primary  coil  is 
decreasing^  then  the  induced  electromotive  force  in  the 
secondary  coil  will  cause  a  current  to  flow  around  in  the 
same  direction  as  the  current  in  the  primary  coil. 


ELECTRICITY  AND  MAGNETISM. 


1589 


2455.  An  induction-coil  is  an  apparatus  devised  on 
the  principle  of  mutual  induction  for  producing  pulsating 
currents  of  electricity  of  high  electromotive  force.  Induc- 
tion-coils are  sometimes  called  Ruhmkorff  coils,  from  the 
name  of  a  celebrated  manufacturer  of  them.  They  consist, 
essentially,  of  two  coils,  primary  and  secondary,  wound 
around  a  core  consisting  of  a  bundle  of  iron  wires.  In  Fig. 
978  the  secondary  coil  is  composed  of   a  large  number  of 


^B 


Fig.  9 


turns  of  fine  insulated  wire,  while  the  primary  coil  P  con- 
tains only  a  few  turns  of  thick  insulated  wire.  The  primary 
circuit  is  automatically  opened  and  closed  at  a  and  i,  in  the 
following  manner:  t  represents  a  spring  which  tends  to 
keep  the  circuit  closed  between  the  armature  a  and  the 
contact  pin  /.  As  soon,  however,  as  the  circuit  is  closed  by 
the  action  of  the  spring,  the  current  from  the  battery  B 
begins  to  circulate  around  the  core  in,  thereby  producing  an 
electromagnet  and  attracting  the  armature  a  away  from 
the  contact  pin  i.  Upon  opening  the  circuit  between  a  and 
?',  the  magnetism  in  the  core  begins  to  weaken,  the  spring 
once  more  closes  the  circuit,  and  the  entire  operation  is 
again  repeated.  These  actions  take  place  in  rapid  succes- 
sion, several  times  a  second,  constantly  producing  a  change 
in  the  lines  of  force  passing  through  the  core,  and  thereby 
inducing  a  current  in  the  secondary  coil. 

2456.  Fig.  979  shows  the  commercial  form  of  Ruhm- 
korff coil.  The  primary  coil  is  wound  around  the  core  of 
soft  iron  wires,  and  its  two  ends  brought  out  at/,  /'.     The 


1590  PRIN.  OF  ELECTRIC.  AND  MAGNETISM. 


secondary  coil,  consisting  of  several  miles  of  fine  insulated 
wire,  is  wound  over  the  primary  coil,  and  its  ends  attached 
to  the  insulated  electrodes  s,  s'.  The  current  in  the 
primary  coil  is  obtained  from  a  voltaic  battery  connected  to 


Fig.  979. 

the  terminals  at  t,  t\  and  is  interrupted  by  means  of  a 
mercury  break  at  A  and  B.  The  apparatus  is  also  provided 
with  a  commutator  C,  which  commutes  or  changes  the  direc- 
tion of  the  current  in  the  primary  coil.  AVhen  a  battery 
which  develops  an  electromotive  force  of  a  few  volts  and 
comparatively  large  currents  is  connected  in  the  primary 
circuit  as  described,  a  torrent  of  sparks  passes  between  s 
and  s\  under  an  electromotive  force  of  several  thousand  volts. 


ELECTRICAL  MEASUREMENTS. 


ELECTROMAGNETIC  MEASUREMENTS. 

24:57,  A  current  of  electricity  is  not  a  material  sub- 
stance, and,  therefore,  has  no  dimensions  (length,  area,  or 
weight)  by  which  it  might  be  measured.  A  ciirrent  oj 
electricity  must,  therefore,  be  measured  by  the  effects  which 
it  prodiices. 

2458.     These  effects  manifest  themselves  as  follows  : 

When  a  current  of  electricity  is  flowing  in  a  conductor,  the 
energy  expended  in  overcoming  the  resistance  of  the  conductor 
manifests  itself  as  heat.  The  amount  of  this  energy  is 
equal  to  the  square  of  the  current  times  the  resistance  (see 
Art.  2341);  therefore,  the  heat  generated  in  a  circuit  will 
be  proportional  to  the  square  of  the  current  if  the  resist- 
ance be  constant,  or  to  the  resistance  if  the  current  be  con- 
stant. 

When  a  current  of  electricity  flozvs  through  a  conducting 
liquid,  the  liquid  is  decomposed.  This  decomposition  is  due 
to  a  chemical  action  of  the  current,  known  as  electrolysis, 
and  is  distinct  from  the.  heating  effect.  The  decomposition 
either  liberates  a  certain  amount  of  gas  or  deposits  one  or 
more  of  the  elements  of  the  liquid  upon  one  of  the  elec- 
trodes. The  amount  of  liquid  decomposed  is  directly  pro- 
portional to  the  quantity  (coulombs)  of  current ;  hence,  the 
rate  of  decomposition,  or  the  amount  of  liquid  decomposed 
per  unit  of  time,  is  proportional  to  the  strength  of  the  cur- 
rent in  amperes. 

When  a  current  of  electricity  floivs  through  a  conductor,  a 
field  of  magnetic  force  is  set  up  around  the  conductor  zvhich 

For  notice  of  copyright,  see  page  immediately  following  the  title  page. 


1592  ELECTRICAL  MEASUREMENTS.  • 

tends  to  produce  a  relative  motion  in  any  other  magnetic 
field  in  the  vicinity ;  as,  for  instance,  that  emanating  from  a 
magnet  pole.  The  force  acting  on  such-  a  pole  will  be 
directly  proportional  to  the  strength  of  the  current,  to  the 
length  of  the  conductor,  to  the  strength  of  the  magnet 
pole,  and  inversely  proportional  to  the  square  of  the  dis- 
tance between  the  conductor  and  the  magnet  pole. 

An  instrument  which  measures  a  current  by  its  electro- 
magnetic effect  is  called  a  galvanometer. 


THEORY    OF    THE    GALVANOMETER. 

2459.  As  the  units  of  electrical  measurements  are 
based  upon  the  so-called  "absolute"  or  "  C.  G.  S."  system 
(see  Art.  2254),  measurements  of  current  by  means  of 
electrolytic  effect  can  be  made  only  when  the,  effect  of  unit 
current  has  been  previously  determined.  By  the  electro- 
magnetic action  the  absolute  value  of  a  current  may  be 
derived  as  folloAvs  : 

As  stated  in  Art.  2458,  the  force  exerted  en  a  unit  pole 
by  a  neighboring  current  is  proportional  to  the  strength  of 
the  current,  to  the  length  of  the  conductor,  to  the  strength 
of  the  pole,  and  inversely  proportional  to  the  square  of  the 
distance  from  the  conductor  to  the  unit  pole. 

Then,  to  exert  unit  force  on  the  unit  pole,  it  is  necessary 
to  employ  unit  current,  and  a  conductor  of  unit  length,  that 
is,  one  centimeter  long,  which  must  be  bent  to  an  arc  of 
unit  (one  centimeter)  radius,  in  order  that  each  part  of  the 
conductor  be  at  unit  distance  from  the  unit  pole. 

Under  these  conditions,  a  current  of  one  C.  G.  S.  unit 
flowing  through  the  conductor  will  act  on  a  unit  pole  at  the 
center  of  the  arc  to  which  the  conductor  is  bent  with  a 
force  of  one  dyne.  Thus  the  absolute  value  of  one  C.  G.  S. 
unit  of  current  may  be  determined. 

2460.  When  a  magnetic  pole  is  placed  near  another 
magnetic  pole,  the  attraction  (or  repulsion)  of  the  two  poles 
is  proportional  to  the  product  of  the  strengths  of  the  two 


ELECTRICAL  MEASUREMENTS.  1593 

poles,  and  inversely  proportional  to  the  square  of  the  dis- 
tance between  them  ;  so,  two  equal  magnetic  poles,  which, 
when  placed  at  a  unit  distance  (one  centimeter)  apart,  exert 
a  force  of  attraction  or  repulsion  on  one  another  of  one  dyne^ 
are  said  to  be  of  tinit  strength. 

2461.  In  Art.  3273  it  was  pointed  out  that  the 
C.  G.  S,  unit  of  current  is  ten  times  greater  than  the  prac- 
tical unit,  the  latter  being  more  convenient  to  use.  Simi- 
larly in  Arts.  2282  and  2303  the  C.  G.  S.  and  practical 
values  of  the  units  of  resistance  and  electromotive  force 
were  given. 

It  would  be  very  difficult  to  construct  apparatus  that 
would  fulfil  the  conditions  given  in  Art.  2459.  It  is  much 
easier  to  vise  a  conductor  bent  into  a  complete  circle,  and  as 
the  effect  of  changing  various  dimensions  is  known  from  the 
relations  given  in  Art.  2459j  a  formula  may  be  constructed 
which  will  give  the  effect  on  a  magnet  pole  of  a  current 
flowing  through  a  conductor  of  any  length  bent  to  any 
radius. 

Let  r  represent  the  radius  in  centimeters  to  which  the 
conductor  is  bent;  now,  if  the  conductor  be  of  sufficient 
length  to  be  bent  into  a  coil  of  more  than  one  turn  having 
a  radius  r,  the  length  of  eacJi  turn  of  the  bent  conductor  is 
Tz  d^=  2  TT  r  centimeters,  and  the  total  length  of  the  con- 
ductor ■^z'^TLrt  centimeters,  where  /  represents  the  number 
of  turns  that  the  conductor  makes  when  bent  into  the  coil. 
The  distance  between  the  conductor  and  the  center  of  the 
coil  is  obviously  equal  to  r  centimeters ;  then  the  force  that 
a  current  of  1  C.  G.  S.  unit  flowing  through  the  coil  would 
exert  on  a  unit  magnet  pole  placed  at  the  center  of  the  coil  = 

• — -^ — •  dynes,  being  directly  proportional  to  the  length  of  the 

conductor,  and  inversely  proportional  to  the  square  of  the 
distance  between  the  magnet  pole  and  the  conductor. 
(Art.  2458.) 

This  force  being  also  directly  proportional  to  the  strength 
of  the  current,  a  current  of  A   C.  G.  S.  units  will  exert  a 


1594  ELECTRICAL  MEASUREMENTS. 

force  oi  A  X ^ —  dynes;  or,  representing  the  force  exerted 

on  the  magnet  pole  in  dynes  by/", 

27:Ari 
-       p— • 

Dividing  both  terms  of  the  fraction  by  r, 
/=^,         (448.) 

which  is  the  formula  required. 

2462.  It  is  not  convenient  to  directly  measure  the 
force  exerted  on  a  unit  pole  by  a  current  circulating  in  a 
coiled  conductor. 

If,  however,  any  magnet  pole  can  be  influenced  by  a 
known  constant  force  in  one  direction,  then,  by  exerting 
upon  it  another  force,  due  to  a  current  circulating  in  a 
coil,  but  acting  in  a  different  direction,  the  resultant  of  the 
two  forces  may  be  accurately  determined  and  the  value  of 
the  second  force  measured. 

This  known  constant  force  is  furnished  by  the  earth 
itself,  which  is  a  magnet  of  such  enormous  size  that  for 
short  distances  the  direction  of  its  lines  of  force  may  be 
considered  as  perfectly  parallel.  The  actual  direction  of  the 
earth's  field  is  not  horizontal,  but  at  an  angle  to  the  hori- 
zontal, so  the  actual  field  may  be  said  to  be  made  up 
of  two  components — a  horizontal  and  a  vertical  component. 
The  horizontal  component  is  most  frequently  made  use  of  in 
measurements,  as  in  this  case.  A  small  bar  magnet  placed 
across  the  earth's  field  of  force  will  have  equal  and  opposite 
forces  acting  on  its  poles  or  ends,  since  the  lines  of  force  act 
in  a  parallel  direction  ;  this  results  in  turning  the  magnet 
about  its  center,  if  the  magnet  is  free  to  move,  until  the 
forces  act  in  a  direct  line  with  the  center,  when  it  can  no 
longer  move.  This  is  illustrated  by  the  magnet  in  the 
common  compass.  The  force  of  the  earth's  field  tends  to 
keep  the  magnet  parallel  to  the  lines  of  force  of  the  earth's 
field,  and,  consequently,  the  magnet  points  7iorth  and  south. 


ELECTRICAL  MEASUREMENTS. 


1595 


2463.     Fig.  980  illustrates  this  action.     The  direction  of 

the  earth's  field  of  force  is  represented  by  the  line  a  b.     A  bar 

magnet,  N  S,  placed  across  this  line  at 

an  angle  with  it  will  have   equal  and 

opposite    forces  acting  upon  the  poles 

N  and   S,    as    shown   by    the    arrows. 

These    forces    may   be    considered    as 

parallel     to    the    line   ad;    so,    if   the 

magnet    be    free    to    turn    about    its 

center,    these   forces    will    bring    it    to 

a    state    of    rest    when    the    line    a  b 

passes    through    the    magnet    from   N 

to  S. 

If  the  magnet  A^^S"  be  acted  upon  by 

another  force  at  an  angle  with  a  b,  the 

magnet    will    come    to  rest  at  a   point 

where  the  two  forces  balance. 

In  Fig.  981  the  magnet  N  S  \s  acted  upon  by  the  earth's 

field  along  the  line  a  b,  the   direction  of  the  force  on  the  N 

pole  of  the  magnet  being  along  the 
line  d  N^  and  that  on  the  5  pole 
along  the  line  a  S,  as  indicated  by 
the  arrow-heads.  In  addition, 
another  force  is  acting  along  the 
line  X  J',  at  right  angles  to  a  b,  the 
direction  of  the  force  on  the  N 
pole  being  along  the  line  c  N,  and 
on  the  vS  pole  being  along  the  line 
d  S,  as  indicated  by  the  arrows. 
Under  the  influence  of  these  two 
forces  the  magnet  is  deflected  into 
the  position  shown,  where  it  re- 
mains at  rest,  making  the  angle  7/1°  with  the  line  a  b. 

Calling  the  horizontal  component  of  the  strength  of  the 

earth's  field  77,  the  strength  of  the  force  acting  along  the 

line  X  y,  /,  and  the  strength   of  each  pole  of  the  magnet 

N  S,p,  then  the  forces  acting  on  the  N  pole  of  the  magnet 

are  equal  to  H  Y.  p  in  the  direction  d  N^  and  f  y.  p  \n  the 


1596  ELECTRICAL  MEASUREMENTS. 

direction  c  N\  the  forces  acting  on  the  S  pole  are  equal  to 
//  X  /  in  the  direction  ^  c^  and  f  X  p  in  the  direction  d  S. 
The  force // X  /  acting  in  the  opposite  directions  on  the  two 
poles  of  the  magnet  form  a  couple  tending  to  rotate  the 
magnet  about  its  center  o.  The  moment  of  this  couple  is 
equal  to  one  of  the  forces  multiplied  by  the  perpendicular 
distance  between  their  lines  of  action.  (See  Art.  906.) 
That  is,  the  moment  of  the  couple  produced  by  the  force  H p 
is  equal  to  H  p  X  c  N^  and  its  direction  is  right-handed. 
Similarly,  the  force  f  p  produces  a  couple  which  tends  to 
produce  left-handed  rotation  of  the  magnet,  and  the  moment 
of  this  couple  is  fp  X  S  c.  Since  the  magnet  is  in  equilib- 
rium, that  is,  at  rest,  these  two  moments  are  equal,  and 

fpxSc=  H  p  XcN,  or/  xSc  =  Hxc  N. 

Since  this  last  equation  does  not  contain  /,  it  follows  that 
the  deflection  of  the  magnet  is  independent  of  the  strength 
of  the  magnet. 

Since /X  Sc=/IXcN,f=II^. 

In  Art.  754,  rule  5,  it  is  stated  that  the  tangent  of  an 
angle  is  equal  to  the  side  opposite  divided  by  the  side 
adjacent. 

In  Fig.  981,  riV  is  the  side  opposite  the  angle  7n°,  and  Sc 

cN 
the   side  adjacent.     Therefore,  -^-^  is  the  tangent  of    the 

angle  w°,  and  the  force  f  is  given  by  the  formula 

f=  Hxt2inm°.  (449.) 

H  being  constant,  f  varies  as  the  tangent  of  the  angle 
through  wJiicJi  the  magnet  is  deflected.  An  instrument  which 
measures  current  on  this  principle  is  called  a  tangent 
galvanometer. 

2464.     The  horizontal   component  (//")  of  the  earth's 

field  has  been  accurately  measured  at  various  places,  and 
the  following  table  gives  the  values  for  some  well-known 
localities : 


ELECTRICAL  MEASUREMENTS. 
TABLE    84. 


1597 


HOKIZOIVTAL  COMPONENT  OF  THE  EARTH'S  MAGNETISM^ 


Localil/. 

Value  of  Compo- 
nent. 
Lines  of  Force 
per  Square  Centi- 
meter. 

London,  England 

Paris 

.180 
.188 

Berlin 

.178 

Rome 

.240 

Montreal 

.147 

Niagara ... 

Halifax 

.167 
.159 

Boston 

.170 

New  York 

.184 

Philadelphia 

.194 

Washington 

.200 

Chicago 

.184 

Cleveland 

.184 

San  Francisco 

.255 

TANGENT   GALVANOMETER. 

2465.  It  is  necessary  that  the  lines  of  force  that  in- 
fluence the  magnet  be  practically  parallel  within  the  range 
covered  by  the  swing  of  the  magnet.  With  the  earth's  field 
this  is  the  case,  as  has  been  pointed  out  in  Art.  2462  ;  but 
with  a  coiled  conductor,  this  only  holds  true  of  a  very  small 
space  relative  to  the  diameter  of  the  coil,  at  the  center  of 
the  coil.  A  tangent  galvanometer  must,  therefore,  have  a 
magnet  of  short  length  as  compared  with  the  diameter  of 
the  coil. 

A  magnet  f  in.  long  can  be  used  with  a  coil  of  8  in. 
diameter  with  accurate  results. 

The  deflections  of  a  magnet  as  short  as  this  could  scarcely 


1598 


ELECTRICAL  MEASUREMENTS. 


be  read  directly.  A  very  thin  light  pointer  is,  therefore,  at- 
tached  to  the  magnet,  usually  at  right  angles  to  it,  which 
extends  out  over  a  scale  upon  which  the  deflections  may  be 
read. 

Fig.  982  gives  a  top  view  of  a  simple  tangent  galvanome- 
ter in  which  N  S  is  the  coil  of  wire  and  F  is  the  pointer  at- 
tached to  the  permanent  magnet  M.     Two  scales  are  shown, 


one  on  each  side  of  the  coil.  One  is  divided  into  degrees, 
and  the  divisions  on  the  other  are  proportional  to  the  tan- 
gents of  the  angles  represented  by  the  divisions  on  the  degree 
scale. 


2466.  In  order  that  a  variety  of  current  strengths  may 
be  measured  with  the  same  instrument,  it  is  customary  to 
wind  the  coil  in  two  or  more  parts,  of  varying  number  of 
turns  and  size  of  wire.  The  terminals  of  these  parts  of  the 
coil  are  led  out  to  binding-posts,  ^,  h,  b,  b,  Fig.  983,  on  the 
base  of  the  instrument,  so  that  either  one  or  all  the  parts  of 
the  coil  may  be  used.  Even  this  method  of  winding  does 
not  give  much  range  to  the  instrument.  Another  way  of 
regulating   its  indications  is  to  vary   the   effective   earth's 


ELECTRICAL  MEASUREMENTS. 


1599 


field,  which  may  be  accomplished  by  placing  a  permanent 
bar  magnet,  called  a  controlling  magnet,  in  the  plane  of 
the  coil  and  parallel  to  it. 

Fig.  983  shows  a  tangent  galva- 
nometer, with  an  adjustable  control- 
ling magnet  m.  If  this  controlling 
magnet  be  so  placed  that  its  ^  pole 
corresponds  in  direction  with  the  N' 
pole  of  the  magnet  of  the  instrument, 
its  field  will  be  added  to  the  earth's 
field,  so  that  a  given  current  will  give 
a  smaller  deflection  than  if  the  con- 
trolling magnet  were  removed.  If  the 
polarity  of  the  controlling  magnet  be 
reversed,  the  opposite  effect  will  re- 
sult, and  the  instrument  will  give  a 
deflection  with  a  very  small  cur- 
rent. FIG.  983. 


2467.  Controlling  magnets  are  used  on  many  forms  of 
galvanometers;  there  is  a  difficulty,  known  as  drift,  which 
attends  their  use,  especially  when  used 
to  make  the  galvanometer  very  sensi- 
tive. This  difficulty  is  due  to  the  fact 
that  the  direction  of  the  earth's  field  is 
continually  changing  slightly,  and  its 
effect  is  to  make  the  zero-point  of  the 
instrument  vary  from  time  to  time. 
This  effect  may  be  shown  by  the  dia- 
gram in  Fig.  984.  In  («),  n  o  represents 
the  direction  and  magnitude  of  the 
force  due  to  the  earth's  field,  and  ii  in 
the  direction  and  magnitude  of  the 
force  due  to  the  controlling  magnet.  The  resultant  n  s  is 
then  the  direction  which  the  magnet  of  the  instrument  would 
assume.  Now  if  the  direction  of  the  earth's  field  change 
through  a  slight  angle  to  the  position  shown  in  (l?),  the  re- 
sultant is  then  the  line  n^  s^,  and  its  direction  is  at  an  angle 


1600  ELECTRICAL  MEASUREMENTS. 

of  nearly  180°  to  the  resultant  11  s.  If  the  controlling  mag- 
net had  not  been  used,  there  would  have  been  a  slight 
"  drift,"  but  the  use  of  the  controlling  magnet  to  lessen  the 
effective  field  very  much  magnifies  the  effect  of  any  change 
in  the  direction  of  the  earth's  field. 

2468.  When  a  controlling  magnet  is  used,  it  is  neces- 
sary to  find  the  deflection  that  a  certain  known  current  will 
produce,  as  the  actual  value  of  II  is  no  longer  known. 
Knowing  the  deflection  with  a  given  current,  other  currents 
may  be  measured,  as  the  galvanometer  is  still  governed  by 
the  same  law,  and  formula  449  may  be  changed  to  read 

C  =  A'  tan  7n°,         (450.) 

where  6^=  current  in  amperes  and /x"  =  a  constant,  called 
the  galvanometer  constant^  by  which  the  tangent  of  the  angle 
of  deflection  must  be  multiplied  to  get  the  value  of  the  cur- 
rent flowing.  This  process  of  finding  the  constant  of  a 
galvanometer  or  other  measuring  instrument  by  comparing 
it  with  a  known  standard  is  called  calibration. 

The  formula  for  the  value  of/" with  this  form  of  tangent 
galvanometer  is  the  same  as  before,  viz.,  _/"=//  tan  111° ,  but 
the  value  of  H  is  now  the  intensity  of  the  earth's  field //wi"  or 
oninus  (according  to  its  polarity)  the  intensity  of  the  field 
due  to  the  controlling  magnet.  After  having  found  the 
galvanometer  constant ^  this  value  of  H  may  be  calculated. 

2469.  The  following  examples  illustrate  the  application 
of  the  formulas  of  the  tangent  galvanometer: 

Example. — What  will  be  the  force  in  dynes  exerted  on  a  unit 
magnet  pole  placed  at  the  center  of  a  coiled  conductor  of  three  turns 
bent  to  a  circle  of  13  cm.  radius,  by  a  current  of  3  C.  G.  S.  units  ? 

Solution. — Use  formula  448,  /  = . 

3 TT  =  6.3833;  A  =  2;  /  =  3;  Ai  =  Q;  r=13. 

^      6.3833x6        37.6993      0^.-,/.^ 

Then,        /= to^—  =  ■ — to —  —  3-1416  dynes.     Ans. 

13  13 

Example. — A  tangent  galvanometer  has  the  following  dimensions: 
Mean  diameter  of  coil,  7|  in. ;  number  turns  first  section,  3;  number 
turns  second  section,  1.     If  this  instrument  is  set  up  in  Boston,  and  a 


ELECTRICAL  MEASUREMENTS.  1601 

current  of  2  amperes*  is  sent  through  the  first  section  of  the  coil,  what 
will  be  the  deflection  of  the  magnet  in  degrees  ? 

Solution. — Use  formula  448,  /= . 

Diameter  of  coil  =  1^  in.  =  20  cm. ;  turns  =  3;  amperes  =  2;  C.  G.  S. 
units  =  .2. 

_        ,          .     2X3.1416X.2X3      3.76992       o^.qqo  ^         ^       .        -i 
Therefore,  /  = -j =  — --r —  =  .376992  dyne  due  to  coil. 

Also,  from  formula  449,  /=  Hx  tan  ;«°. 

Transposing,  tan  jn"  =  ■£-.     JI=.11iO.     (Table  84.) 

rru       f         .  o       .376992      „_._ 

Therefore,  tan  m   =  — .„^     =  2.2176. 
.1  (U 

Referring  to  the  table  of  Natural  Tangents,  the  tangent  of  the 
angle  05°  46'  is  2.22164.  This  is  as  nearly  correct  as  the  deflection  could 
be  read  on  the  scale.  Ans.  65°  46',  nearly. 

24'70.  Example. — Another  galvanometer  is  constructed  exactly' 
like  that  referred  to  in  Art.  3469,  but  with  a  controlling  magnet 
attached  to  increase  its  range.  The  two  galvanometers  are  connected 
together  by  wires,  so  that  the  second  seciwjt  of  the  coil  of  the  Jlrsi 
galvanometer  (called  No.  1)  is  in  series  with  the  first  sectwtt  of  the 
galvanometer  with  the  controlling  magnet  (called  No.  2).  On  sending 
a  current  through  the  two  instruments,  the  deflection  of  No.  1  is  52°, 
while  the  deflection  of  No.  2  is  but  38°.  (a)  What  current  is  passing 
through  the  galvanometers,  and  {b)  what  is  the  value  of  .the  galvanom- 
eter constant  of  No.  2,  if  the  experiment  is  made  in  Philadelphia  ? 

Solution. — (a)  Consider  No.  1  only. 

From  formula  449,  /=  Hta.nm°. 

As  H—  ,194,  7n°  =  52°,  and  tan  m"  =  1.28,  nearly, 

/=.194x  1.28  =  .24832. 

Also,   from   formula  448, /=  ^^^^,  or  ^^11^=.  24832;    hence, 

6  2832  V  v4  V  1 

-^ j^ ^^  =  .24832;  .62832^  =  .24832,  and  A  =  .3952  C.  G.  S.  units 

of  current. 

As  A  equals  C.  G.  S.  units,  this  result  must  be  multiplied  by  10  to 
give  practical  units  =  3.952  amperes.     Ans. 

(d)  In  No.  2  the  current  is  3.952  amperes  and  the  tangent  of  the 
angle  of  deflection  ~  tan  38°  =  .7813,  nearly  ;  substituting  in  formula 


*  Whenever  the  word  ampere  is  used  alone,  the  practical  unit 
(one-tenth  of  the  C.  G.  S.  unit)  is  understood.  The  C.  G.  S.  unit,  when 
used,  is  called  the  C  G.  S.  unit. 


1602  ELECTRICAL  MEASUREMENTS. 

450,  C=  A^tan  m°  ;  (:'=  3.953,  and  tan  m"  =  .7813,  3.952  =  A'X  .TOIS, 
8.952 


.7813 


A' =5.058.     Ans. 


Remark. — This  value  of  A' is  only  good  for  the  first  section  of  the 
galvanometer  coil,  which  consists  of  three  turns.  If  the  value  of  H  in 
formula  449,/=  H  tan  ;«%  be  calculated  for  this  galvanometer,  then 
changes  may  be  made  in  the  number  of  turns  of  the  coil  used,  without 
recalculating  a  galvanometer  constant,  if  the  controlling  magnet  be 
unchanged. 

In  the  example  above  given,  the  value  oifirv  No.  2  is  obviously  three 

times  that  in  No.  1,  as  the  same  current  passes  through  three  times  the 

length  of  wire.     Therefore,  /=  3  X  .24832  =  .74496,  and  tan  m°  —  tan. 

f  744qfi 

38°  =  .7813,  nearly.     As      ■'     ,  =  H,  then,  '  JT:  "  =  AT  =  .9535. 
■'  tan;«  .7813 

This  value  of  H  represents  the  combined. value  of  the  field  due  to 

the  earth  and  that  due  to  the  controlling  magnet.     As  will  be  seen,  the 

intensity  of  this  field  is  nearly  five  times  that  of  the  earth  alone ;  so 

galvanometer  No.  2  may  be  used  to  measure  currents  of  about  five 

times  the  strength  that  No,  1  will  measure  under  the  same  conditions. 


EXAMPLES    FOR    PRACTICE. 

2471.  1.  A  coil  of  wire  is  wound  20  cm.  in  diameter  and  con- 
sists of  5  turns.  Through  this  coil  a  current  of  12  amperes  is  passed. 
What  will  be  the  force  exerted  on  a  unit  magnet  pole  at  the  center  of 
the  coil  ?  Ans.  3.77  dynes. 

2.  Using  the  galvanometer  (Art.  3469),  a  current  of  5  amperes  is 
passed  through  the  second  section  of  the  coil,  {a)  What  will  be  the 
deflection  in  degrees  ?  {b)  What  would  be  the  deflection  if  the  instru- 
ment were  in  Washington  instead  of  Boston  ?  (c)  What  current  would 
a  deflection  of  46°  indicate,  using  the  first  section  of  the  coil  and  taking 
the  measurement  in  Chicago  ?  i  (a)  61°  35',  nearly. 

Ans.  ]  \b)  57°  31',  nearly. 

( {c)  1.01  amperes,  nearly. 

3.  A  galvanometer  with  a  coil  12  in.  diameter  having  12  turns  of 
wire  gives  a  deflection  of  42°  when  a  certain  current  is  passed  through 
the  instrument  being  set  up  in  Montreal.  What  is  the  value  of  this 
current  in  amperes  ?  Ans.  .267"  ampere. 

SINE   GALVAIVOMETER. 

2472.  Another  form  of  galvanometer,  shown  in  Fig. 
985,  employs  much  the  same  principle  as  the  tangent  gal- 
vanometer, except  that  its  coil  C  is  movable  about  a  verti- 
cal axis. 


ELECTRICAL  MEASUREMENTS. 


1603 


This  instrument  being  set  up  with  the  plane  of  its  coil  in 
the  earth's  magnetic  meridian,  and  the  pointer  (which,  as  in 
the  tangent  galvanometer,  is  usually  fixed  at  right  angles  to 
the  magnet)  at  zero,  a  current  is  sent  through  the  coil  by- 
means  of  the  wires  W,  which  deflects  the  magnet.  The  coil 
is  then  turned  in  the  same  di- 
rection that  the  magnet  is  de- 
flected, until  in  such  a  position 
that  the  magnet  comes  to  rest 
with  the  plane  of  the  coil  coin- 
ciding with  the  direction  of  the 
magnet.  This  point  is  usually 
determined  by  a  mark  on  a 
part  of  the  support  of  the  coil, 
which  must  be  made  to  register 
with  the  pointer  attached  to 
the  magnet.  The  angle  through 
which  the  coil  has  been  turned 
is  read  by  a  vernier  from  a  scale 
of  degrees  .S  attached  to  the 
base  of  the  instrument,  and  tJie 
sine  of  this  angle  multiplied  by 
the  proper   constant   gives    the  fig.  985. 

current  flowing  in  the  coil^  whence  the  name. 


2473.  The  theory  of  the  sine  galvanometer  may  be 
demonstrated  as  follows: 

In  Fig.  986,  NS  is  a  magnet  which  is  acted  on  by  the 
earth's  field  along  the  line  a  b,  the  direction  of  the  force  on 
the  N  pole  being  represented  by  the  line  Nc.  Another 
force  is  also  acting  on  the  magnet  at  right  angles  to  its  axis 
NS,  along  the  line  xy.  This  force  acts  on  the  N  pole  in 
the  direction  represented  by  the  line  N  d.  As  the  forces 
acting  on  the  S  pole  are  equal  to  those  acting  on  the  N  pole, 
only  the  latter  need  be  considered. 

As  before,  call  the  horizontal  component  of  the  strength 
of  the  earth's  field  H,  the  strength  of  the  force  acting  along 
the  line  .arj, /,and  the  strength  of  the  pole  of  the  magnet,/. 


1604 


ELECTRICAL  MEASUREMENTS. 


Let  the  line  N  c  represent  the  amount  and  direction  of 
the  force  H p  due  to  the  earth's  field,  and  the  line  N dxho. 
amount  and  direction  of  the  other  force;  then,  by  comple- 
ting the  parallelogram  of 
forces  (see  Art.  875)  the  re- 
sultant of  the  two,  N  c,  is 
found. 

This  resultant  N  e  repre- 
sents the  direction  and 
amount  of  the  single  force 
that  would  deflect  the  mag- 
net to  the  position  shown, 
where  it  makes  the  angle  vi° 
with  the  line  N c^  which  is 
parallel  to  a  b. 

It  is  evident  that  the 
lengths  N c  and  A^</  can  rep- 
resent H  diVidf,  respectively, 
since  they  have  been  assumed 
to  represent  those  amounts 
each  multiplied  by  the  constant  /.  Then,  as  Nd=  c  e  and 
N  d  —  f,  f=ce.  From  Art.  754,  rule  2,,  c  e  ~  N  c  'SAXim°  \ 
hence,  as /=<:<?  and //"=  TV ^, 


f=H. 


(451.) 


Note. — This  principle  may  also  be  demonstrated  by  the  use  of 
couples,  as  in  the  case  of  the  tangent  galvanometer,  and  it  is  recom- 
mended that  the  student  work  out  that  demonstration  himself. 


The  value  of /"may  be  obtained  in  the  same  manner  as 
for  the  tangent  galvanometer. 

If  a  magnet  be  used  whose  length  is  nearly  equal  to  the 
inside  diameter  of  the  coil,  the  current  will  still  be  propor- 
tional to  the  sine  of  the  angle  of  deflection  of  the  needle,  as 
the  axis  of  the  needle  is  always  at  right  angles  to  the  lines 
of  force  of  the  coil,  but  the  value  of/ will  no  longer  be  cor- 
rect if  calculated  from  formula  448,  as  the  force  acting  on 
the   magnet   poles   is   not    uniform    throughout    the    area 


ELECTRICAL  MEASUREMENTS.  1605 

enclosed  by  the  coil,  but  is  greater  near  the  coil  than 
towards  the  center,  and  formula  448  gives  the  force  at  the 
center  only. 

The  sine  galvanometer  is  not  as  convenient  an  instru- 
ment to  use  as  the  tangent  galvanometer,  as  the  coil  must 
be  carefully  adjusted  to  the  correct  position  to  get  accurate 
results  instead  of  taking  the  reading  directly  from  the  posi- 
tion of  the  pointer,  but  it  is  more  accurate  than  ordinary 
forms  of  tangent  galvanometers. 


REFLECTING   TANGENT  GALVANOMETER. 

2474.  If  the  needle  of  a  tangent  galvanometer  be  sus- 
pended by  a  fiber  of  raw  silk  or  other  similar  material  with- 
out twist,  and  if  a  beam  of  light  reflected  from  a  small 
mirror  attached  to  the  needle  be  used  for  a  pointer,  very 
accurate  measurements  of  the  deflection  can  be  obtained. 

An  instrument  so  constructed  is  known  as  a  reflecting 
tangent  galvanometer.  It  is  usual  in  this  case  to  set 
up  a  suitably  divided  straight  scale  some  distance  from,  and 
parallel  to,  the  normal  (zero)  position  of  the  mirror.  The 
lamp  giving  the  light  is  located  behind  the  scale,  in  which 
is  a  small  slit  or  hole  through  which  the  necessarily  small 
beam  of  light  passes,  being  reflected  from  the  mirror  back 
to  the  scale. 

Since  the  reflected  beam  of  light  makes  the  same  angle 
with  the  mirror  that  the  original  beam  does,  but  on  the 
opposite  side  of  a  perpendicular  to  the  mirror,  the  angle 
between  the  original  beam  and  the  reflected  beam  will  be 
equal  to  twice  the  angle  of  deflection  of  the  mirror.  Allow- 
ance for  this  fact,  also  for  the  fact  that  a  straight  scale  is 
used,  must  be  made  in  calculating  the  constant  of  a  reflect- 
ing tangent  galvanometer. 

It  is  usual  in  this  class  of  instruments  to  make  the  mag- 
net of  a  number  of  small  magnets,  made  from  short  bits  of 
steel  needles  or  pieces  of  watch-spring,  and  arrange  one- 
half  of  the  magnets  with  their  poles  opposing  the  remain- 
der, which  makes  the  magnet  astatic ;  that  is,  the  earth's 
field  has  almost  no  directive  force  on  the  magnetic  system 


1606  ELECTRICAL  MEASUREMENTS. 

of  the  instrument.  By  using  a  strong  controlling  magnet, 
the  instrument  is  made  almost  independent  of  the  earth's 
field,  and  thus  errors  or  drift  due  to  variations  in  the  hori- 
zontal component  of  the  earth's  magnetism  are  rendered  of 
little  effect. 

2475.  When  the  magnetic  system  and  mirror  are  thus 
constructed  and  suspended  by  a  long  fiber,  considerable 
difficulty  in  reading  may  be  met  with,  owing  to  the  length 
of  time  required  for  the  needle  to  come  to  rest  after  being 
deflected.  This  is  corrected  by  damping  the  moving 
parts  of  the  instrument,  which  may  be  effected  by  sus- 
pending from  the  needle  a  small  fan  of  very  light  construc- 
tion, which,  by  reason  of  the  friction  of  the  air  on  the 
blades  of  the  fan  as  it  moves,  causes  the  needle  to  swing 
more  slowly  and  come  to  rest  at  once. 

This  damping  effect  is  an  important  feature  of  most 
measuring  instruments.  Other  methods  than  that  given 
above  are  used,  one  of  which  is  to  enclose  the  moving  mag- 
netic needle  in  a  cavity  in  a  block  of  copper;  movement  of 
the  needle  then  sets  up  little  eddy  currents  in  the  copper 
block,  which  retard  the  movement  of  the  needle,  giving 
the  desired  damping  effect. 

In  the  D'Arsonval  galvanometer,  described  in  the  follow- 
ing article,  the  damping  of  the  moving  coil  is  effected  by 
winding  that  coil  on  a  bobbin  of  thin  copper  or  other  non- 
magnetic metal.  The  movement  of  this  bobbin  with  the 
coil  through  the  field  generates  eddy  currents  in  the  bobbin 
itself,  which  currents  produce  the  required  damping  effect. 


THE  D'ARSONVAL,  GALVANOMETER. 

247'6.  Another  electromagnetic  measuring  instrument 
which  is  quite  extensively  used  is  the  D'Arsonval  gal- 
vanometer, which  derives  its  name  from  its  inventor,  a 
French  physicist.  Its  principle  is  slightly  different  from 
most  of  the  other  forms  of  galvanometers  in  that  the  mag- 
net is  large  and  stationary,  and  the  coil  is  small  and  mova- 
ble. It  consists  of  a  large  permanent  horseshoe  magnet, 
between    the    poles  of  which   is  suspended    a   coil  of  wire. 


ELECTRICAL  MEASUREMENTS. 


1607 


Current  is  led  to  the  coil  by  means  of  the  suspension,  and 
this  current  in  the  coil  causes  the  coil  to  rotate  about  its 
axis,  the  tendency  of  the  coil  being  to  place  itself  at  right 
angles  to  the  lines  of  force.  This  tendency  is  opposed  by 
the  suspension,  which  may  be  a  spring  or  an  elastic  wire  or 
fiber.  A  pointer  may  be  attached  to  the  coil  to  indicate  its 
deflection,  though  usually  a  mirror  is  used,  a  reflected 
beam  of  light  from  which  forms  the  pointer,  as  in  the  re- 
flecting tangent  galvanometer.  In  many  forms  of  this 
instrument  a  soft  iron  core  is  supported  between  the  poles 
of  the  magnet,  a  space  being  left  between  the  core  and  the 
magnet  in  which  the  coil  swings.  This  core  serves  to 
increase  the  strength  of  the  field  in  which  the  coil  moves. 

By  suitably  shaping  the  poles  of  the  magnet,  the  intensity 
of  the  magnetic  field  in  various  parts  may  be  so  varied  that 
the  movement  of  the  beam  of  light  will  be  directly  propor- 
tional to  the  current  in  the  coil.  Fig.  987  represents  one 
form  of  the  D'Arsonval  gal- 
vanometer. In  the  figure, 
PP  is  the  magnet;  C^  the 
movable  coil;  5,  vS,  fine  plat- 
inum wires,  which  suspend 
the  coil  C\  M,  the  mirror, 
and  /,  the  iron  core,  which 
is  supported  from  the  back 
in  the  center  of  the  coil  C. 
Connection  from  the  binding- 
posts  B,  B  to  the  coil  C  is 
made  through  the  platinum 
suspension  wires  5",  S.  One 
of  the  chief  advantages  of 
this  instrument  is  the  fact 
that  external  fields,  such  as 
the  earth's  magnetism,  have 
little  effect  upon  it,  so  that  '  '    '"  , 

it  requires  no  controlling  magnet  or  correction  for  the 
earth's  field,  and  may  be  used  near  dynamos  and  large 
masses  of  iron  without  being  affected. 


1608 


ELECTRICAL  MEASUREMENTS. 


Many  of  the  commercial  forms  of  portable  instruments 
are  built  on  the  principle  of  this  galvanometer,  as  will  be 
described. 


REFLECTING   GALVANOMETER. 

247'7'.  It  is  often  desirable  to  use  an  instrument  for 
indicating  the  presence  of  very  small  currents  without 
necessarily  measuring  their  value.  For  this  purpose,  the 
reflecting  tangent  galvanometer  is  modified  by  making  the 
coils  of  considerably  less  diameter  in  proportion  to  the 
length  of  the  magnet,  and  by  winding  the  coil  with  a  great 


Fig.  988. 
many  turns  of  wire,  so  as  to  make  a  very  strong  field  at  the 
center  of  the  coil  with  a  feeble  current.  The  magnetic 
system  is  made  astatic,  but  the  magnets  that  point  in  one 
direction  are  hung  considerably  below  those  that  point  in 
the  opposite,  and  each  set  of  magnets  has  its  own  coil;  in 
order  that  the  magnetic  system  may  be  suspended  in  the 
center  of  the  coils,  each  coil  is  wound  in  two  equal  parts, 
and,  when  mounted,  a  very  small  space  is  left  between  the 
parts,  through  which  the  fiber  which  suspends  the  system 
passes. 


ELECTRICAL  MEASUREMENTS.  1609 

This  form  of  instrument  is  known  as  a  reflecting  gal- 
vanometer. Fig.  988  shows  one  form  of  this  instrument, 
with  lamp  and  scale. 

BALLISTIC   GALVANOMETER. 

24T8.  A  special  form  of  reflecting  galvanometer  known 
as  a  ballistic  galvanometer  is  used  for  measuring  tran- 
sient currents,  such  as  are  induced  in  a  conductor  if  a 
current  in  a  neighboring  conductor  be  started  or  stopped, 
or  if  a  magnet  be  moved  in  the  vicinity.  This  form  of  gal- 
vanometer has  its  magnetic  system  constructed  so  as  to  be 
of  considerable  weight,  and  so  arranged  as  to  give  the  least 
possible  damping  effect.  If  a  momentary  current  pass 
through  the  coils  of  the  instrument,  the  impulse  given  to 
the  needle  does  not  cause  appreciable  movement  of  the  mag- 
netic system  until  after  the  current  has  ceased,  owing  to  the 
inertia  of  the  heavy  moving  parts,  which  results  in  a  slow 
swing  of  the  system  after  the  impulse  has  ceased;  the  max- 
imum angle  of  swing  may  be  read  by  watching  the  spot  of 
light,  reflected  from  the  mirror  attached  to  the  magnetic 
system,  move  across  a  suitably  divided  scale,  and  noting  the 
point  at  which  the  spot  of  light  ceases  to  move  and  begins 
to  swing  back.  The  quantity  of  electricity  (the  number  of 
coulombs)  that  pass  through  the  coils  of  the  instrument  is 
proportional  to  the  sine  of  one-half  the  aitgle  of  deflection  of 
the  needle: 

Q  =  Ks{n'^.  (452.) 

The  deflection  being  usually  small,  the  quantity  of  elec- 
tricity may  be  regarded  as  directly  proportional  to  the  angle 
of  deflection.  As  the  use  of  the  mirror  and  ray  of  light  as  a 
pointer  merely  doubles  the  angle  of  deflection,  it  will  intro- 
duce no  serious  error  to  consider  the  quantity  of  electricity 
proportional  to  the  swing  of  the  spot  of  light  across  the 
scale,  and  formula  452  may  be  modified  to  read 

Q  =  Kd,  (453.) 

where  d  ^=  deflection  in  scale  divisions. 


1610 


ELECTRICAL  MEASUREMENTS. 


2479o     Fig.  989  shows  one  form  of  ballistic  galvanom- 
eter in  which  C,  C^  are  the  two  parts  of  the  coil,  either  oi 


B  P 


Fig.  969. 

which  may  be  swung  back,  as  shown,  to  examine  or  remove 
the  magnetic  system. 

Each  coil  is  supported  from  a  brass  strip,  both  of  which 
are  clamped  in  place  by  the  nut  N. 

Connections  to  the  coils  are  made  from  the  terminals 
P,  P^,  the  coils  being  connected  together  through  the  flexible 
cable  F,  which  allows  either  coil  to  be  swung  aside  without 
disturbing  the  connections. 

When  in  use,  the  instrument  is  surrounded  by  a  case  (not 
shown)  through  which  the  binding-posts  B,  B^  project. 

The  magnetic  system,  an  enlarged  section  of  which  is 
shown  at  the  right,  is  suspended  by  a  fine  quartz  fiber  from 
the  torsion  head  7",  the  magnets  and  mirror  being  hooked 
on  to  the  lower  end  of  the  suspension  by  the  hook  /. 

The  magnets  are  thimble-shaped,  and  filled  with  lead  to 
give  weight.  The  system  is  rendered  astatic  by  the  ar- 
rangement of  polarities  as  shown,  the  upper  and  lower 
magnets  being  the  stronger,  and,  therefore,  directing  the 
system.  No  external  controlling  magnet  is  used  with  this 
system,  so  drift  is  very  nearly  eliminated;  the  sensibility  of 
the  system  is  varied  by  screwing  the  small  soft  iron  ring  W 


ELECTRICAL  MEASUREMENTS.  1611 

up  or  down  on  the  lower  magnet.  If  the  ring  is  screwed 
up,  it  short-circuits  some  of  the  lines  from  that  magnet, 
thus  weakening  its  effect  on  the  system. 

2480.  One  of  the  principal  uses  to  which  the  ballistic 
galvanometer  is  put  is  measuring  the  magnetic  qualities 
of  iron. 

Samples  of  the  iron  to  be  tested,  usually  in  the  form  of  a 
ring,  are  wound  throughout  their  length  with  insulated 
wire,  so  that  if  a  steady  current  be  sent  through  the  wire 
the  ring  will  be  magnetized.  If  a  second  coil  of  wire  be 
wound  for  a  short  distance  over  the  first  coil,  any  change  in 
the  number  of  lines  of  force  in  the  ring  will  induce  an  elec- 
tromotive force  in  the  second  coil. 

A  ring  so  wound  is  represented  in  Fig.  990,  where  R  is 


Fig.  990. 


the  iron  ring,  P  P^  the  primary  or  magnetizing  coil,  5"  5"  the 
secondary  or  induction  coil. 

If  the  coil  S  S  be  closed  through  a  circuit  of  fixed  resist- 
ance^ the  number  of  coulombs  of  electricity  that  will  flow  in 
this  secondary  circuit  zvhen  the  number  of  lines  of  force  pass- 
ing through  that  coil  is  changed  will  be  directly  proportional 
to  the  amount  of  change  in  the  number  of  lines  of  force. 

This  is  independent  of  the  rate  of  change ;  for,  assuming 
that  the  number  of  lines  of  force  changes  uniformly  for  one 
second,  and  that  the  turns  of  the  secondary  coil  are  such 
that  1  volt  is  generated  in  that  coil,  then,  if  the  resistance 
of  the  entire  secondary  circuit  is  1  ohm,  1  ampere  will  flow 
for  1  second,  or  as  long  as  the  E.  M.  F.  is  being  generated; 


1G12  ELECTRICAL  MEASUREMENTS. 

that  is,  the  quantity  of  electricity  will  be  one  coiclonib.  Now, 
if  the  number  of  lines  of  force  be  changed  by  the  same 
amount,  but  in  two  seconds,  only  -i-  volt  will  be  generated 
in  the  secondary  coil,  and  only  ^  ampere  will  flow  in  the 
secondary  circuit,  but  it  will  flow  for  two  seconds,  and  the 
quantity  of  electricity  will  be  the  same  as  before. 

The  same  holds  true  if  the  rate  of  change  in  the  number 
of  lines  is  not  uniform,  which  is  usually  the  case. 

2481.  If  known  currents  be  sent  through  the  primary 
<!;oil  P  P^y  the  magnetizing  force  H  may  be  readily  calculated. 
(See  formula  430.)  Any  change  in  this  magnetizing  cur- 
rent will  produce  a  change  in  the  number  of  lines  of  force 
in  the  iron  ring,  which  will  be  indicated  by  a  swing  of  the 
galvanometer  needle,  and  the  amount  of  this  swing  will  in- 
dicate the  relative  amount  of  change  in  the  number  of  lines 
of  force  passing  through  the  secondary  coil.  For  calibra- 
ting the  ballistic  galvanometer  for  magnetic  measurements, 
it  is  usual  to  note  the  swing  when  a  known  number  of  lines 
of  force  is  made  to  cut  the  turns  of  a  coil  in  the  galvanom- 
eter circuit.  This  may  be  done  by  preparing  a  coil  of 
wire  wound  on  a  bobbin  of  considerable  size,  and  arranging 
it  between  supports  so  that  it  may  be  rotated  through  180°; 
by  placing  the  coil  with  its  plane  at  right  angles  to  the 
direction  of  either  the  vertical  or  the  horizontal  component 
of  the  earth's  magnetism,  the  rotation  of  the  coil  will  cause 
its  sides  to  cut  the  lines  of  force  of  the  earth's  field.  If  the 
value  of  the  component  be  known,  the  number  of  lines  en- 
closed by  the  coil,  and,  therefore,  the  number  cut  by  its 
rotation,  can  be  calculated,  the  area  of  the  space  enclosed 
by  the  coil  being  known.  This  method,  known  as  the  earth 
coil  method,  is  open  to  the  objection  that  the  components  of 
the  earth's  magnetism  vary  slightly  from  time  to  time. 

2482.  Another  method  for  determining  the  magnetic 
properties  of  iron  is  shown  in  Fig.  991,  where  the  apparatus 
and  connections  are  indicated.  The  iron  to  be  tested  is  in 
the  shape  of  a  flat  iron  ring  /,  upon  which  is  evenly  wound 
a  certain  known  number  of  turns  of  insulated  wire,  the 


ELECTRICAL  MEASUREMENTS. 


1G13 


terminals  being/  and/'.  This  is  called  the  primary  or  chief 
coil.  The  same  number  of  turns  of  insulated  wire  are  wound 
on  a  wooden  or  other  non-magnetic  core,  with  the  terminals 
at  t  and  /'.  The  coil  C  is  called  the  calibrating  coil.  On 
the  iron  ring  /and  also  at  the  center  of  the  length  on  the 
coil  C  are  wound  induction-coils,  or  secondary  coils,  consist- 
ing of  a  few  turns  of  insulated  wire. 

As  the  dimensions  of  the  coil  C  and  the  current  passing 
through  the  coil  are  measurable,  the  exact  number  of  lines 
of  force  per  square  inch  designated  by  H  in  air,  wood,  or 
other  non-magnetic  medium,  may  readily  be  determined  by 
formula  430.     According  to  Art.  2478  and  formula  453, 


Fig.  991. 


the  setting  up  of  a  certain  number  of  lines  of  force  in 
the  wooden  core  of  C  will  cause  the  needle  of  the  ballistic 
galvanometer  G'  to  give  a  certain  kick.  By  varying  the 
make  and  break  currents,  the  ballistic  galvanometer  G'  may 
be  calibrated,  so  that  the  kick  of  the  galvanometer  G'  being 
given,  the  number  of  lines  of  force  in  the  coil  C\  or  in  any 
other  similar  coil,  may  be  determined. 

A  succession  of  currents  of  different  values  may  be  sent 
through  the  primary  coil  P  of  the  iron  ring  /,  thus  produ- 
cing therein  a  certain  number  of   lines  of  force   B,  which 


1614  ELECTRICAL  MEASUREMENTS. 

number  is  indicated  by  the  kick  of  the  needle  of  the  balHstic 
galvanometer,  as  previously  noted.  These  results  may  be 
tabulated,  or  else  laid  out  in  the  form  of  a  magnetization 
curve,  as  was  explained  in  Art.   2402. 

2483.  As  the  diagram  now  stands,  the  calibrating  coil 
is  out  of  circuit,  and  the  primary  coil  P  of  the  iron  ring  is 
being  energized  by  the  battery  B.  The  energizing  current 
is  regulated  by  the  adjustable  resistance  i?,  and  is  calculated 
from  the  dimensions  of  the  primary  circuit  or  measured  by 
the  galvanometer,  or  low  reading  ammeter,  G.  The  re- 
versing switch //"is  used  to  start,  stop,  or  reverse  the  current 
in  the  primary  coil  P.  An  adjustable  resistance  R  is  also 
in  the  secondary,  for  varying  the  range  of  the  ballistic  gal- 
vanometer G\  as  the  values  of  H  and  B  are  widely  different. 

In  order  to  calibrate  the  ballistic  galvanometer  G\  the 
reversing-switch  terminals  are  disconnected  from  the  coil  P 
by  means  of  the  double-throw  switch  D,  which  then  enables 
connection  to  be  made  instead  to  the  terminals  /,  /'  of  the 
calibrating  coil  C. 

2484.  The  test  of  the  iron  may  be  made  in  a  variety 
of  ways.  The  two  most  used  are  the  step-by-step  and  the 
reversal  methods. 

The  step-by-step  method  consists  of  suddenly  increas- 
ing or  decreasing  the  magnetizing  current  in  the  primary 
coil  by  moving  the  handle  of  the  rheostat  R.  The  swing  of 
the  galvanometer  G'  at  each  step  indicates  the  amount  of 
change  in  the  lines  of  force  corresponding  to  a  change  in 
the  magnetizing  force.  The  total  number  of  lines  at  any 
point  may  be  determined  by  adding  together  the  previous- 
changes,  as  observed  by  the  swing  of  the  galvanometer. 

2485.  The  reversa*  method  is  to  reverse  the  current 
in  the  primary  by  throwing  the  reversing  switch  H.  The 
lines  of  force  will  then  change  from  a  certain  number  in  one 
direction  down  to  zero,  and  then  to  about  the  same  number 
in  the  opposite  direction.  This  change  will  cause  a  swing 
of  the  galvanometer  6"',  and  one-half  this  swing  is  taken  to 
represent  the  number  of  lines  of  force  in  the  circuit  due  to 


ELECTRICAL  MEASUREMENTS.  1615 

the  magnetizing  force  that  has  been  reversed.  By  increas- 
ing or  decreasing  this  magnetizing  force  by  successive  steps, 
and  reversing  each  time,  the  curve  of  magnetization  may  be 
obtained. 

2486.  One  objection  to  the  step-by-step  method  is  that 
an  error  in  one  of  the  early  observations  will  be  included  in 
the  whole  series,  as  they  are  all  added  together;  but  with 
care  in  taking  the  readings,  this  need  not  occur.  With  the 
method  of  reversals,  however,  the  rcsid2ial  viagnetisni  intro 
duces  an  error;  as,  when  the  magnetizing  force  is  reversed^ 
the  lines  of  force  will  not  also  be  entirely  reversed,  so  that 
there  will  not  be  as  many  lines  in  the  circuit  after  the  re- 
versal as  before,  with  the  same  magnetizing  force.  In  either 
case,  the  magnetizing  force  H  can  be  readily  calculated  from 
the  magnetizing  current,  and  the  total  induction  in  the 
sample  of  iron  may  be  determined  by  the  galvanometer 
swings.  By  this  means  the  value  of  B  maybe  obtained,  and 
the  magnetization  curve  of  the  particular  sample  of  iron 
under  test  may  be  plotted. 

Example. — 1.  Calibrate  the  ballistic  galvanometer  G' ,  shown  in 
Fig.  991,  for  resistance  of  rheostat  7?'  =  0;  500  ohms;  1,000  ohms,  the 
following  information  being  given: 

Data. — The  upper  terminals  of  the  reversing  switch  H  were  dis- 
connected from  the  primary  coil  P  and  connected  to  the  calibrating 
coil  C  by  the  terminals  /,  /',  so  that  the  current  from  the  battery  B 
passed  through  the  calibrating  coil  C,  the  primary  coil  P  being  out  of 
circuit. 

The  elements  of  the  present  primary  circuit  have  resistances 
as  follows: 

Resistance  of  primary  calibrating  coil  C  =  3  ohms. 

Internal  resistance  of  battery  ^  =  1.2  ohms. 

Resistance  of  rheostat  R,  ten  steps  of  4  ohms  each  =  40  ohms. 

Resistance  of  balance  of  primary  circuit,  including  connections,  = 
1.1  ohms. 

The  parts  of  the  secondary  circuit  have  the  following  resistances: 

Resistance  of  rheostat  7?',  ten  steps  of  200  ohms  each  =  2,000  ohms. 

Resistance  of  ballistic  galvanometer  G'  =  500  ohms. 

Resistance  of  balance  of  secondary  circuit,  including  both  secondary 
coils,  =  10  ohms. 

The  battery  P  has  6  cells,  each  furnishing  a  constant  E.  M.  F,  of 
1.9  volts. 


1616  ELECTRICAL  MEASUREMENTS. 

The  secondary  coil  5  consists  of  120  turns  of  No.  22  insulated  wire. 

The  calibrating  coil  C  is  wound  on  a  wooden  rod  30  inches  long  and 
2  inches  in  diameter,  and  consists  of  1,200  turns  of  No.  18  insulated 
wire,  wound  evenly  in  two  layers. 

The  secondary  calibrating  coil  C ,  wound  at  the  center  of  the  length 
of  the  primary  calibrating  coil  C,  has  260  turns  of  No.  22  wire. 

The  ballistic  galvanometer  G'  is  of  the  type  already  described  in 
Art.  2477,  with  a  scale  about  4  feet  long,  and  reads  from  zero  at  the 
center  to  225  at  each  end.  The  resistance  R'  all  being- cut  out,  the 
galvanoDieter  G'  gives  the  scale  reading  J^S. 

Solution. — To  calibrate  the  ballistic  galvanometer  G  means  to 
ascertain  the  deflection  of  the  galvanometer  corresponding  to  one  line 
of  force  passing  through  the  secondary  coil  S. 

The  current  in  the  primary  calibrating  coil  C,  according  to  Ohm's 

law,  is 

„      E  6x1.9  11.4      „_ 

^  =  ^  ^3  + 1.2  + 1.1^ -573-^^-^^  ^"^P"^"^- 

The  number  of  lines  of  force  per  square  inch  cross-section  of  the 
wooden  core,  by  formula  430, 

,,      3.192  X^-'^"       3.192x2.15x1,200      ^„,  ^  .     ^ 

H  = J = -^ =  274.5  per  square  mch. 

The  total  number  of  lines  of  force  in  the  wooden  core  N  =  H  X  area  = 
274.5  X  3.1416  r^  =  274.5  X  3.1416  =  862.4  total  lines  of  force  in  core. 

We  have  now  determined  the  total  number  of  lines  of  force  that 

passed  through  the  secondary  coil  C  of  260  turns  when  the  ballistic 

galvanometer  G'  moved  48  scale  divisions.     If  there  was  only  one  turn 

in  the  secondary  coil  C'  instead  of  260,  the  galvanometer  G'  would 

48 
have  moved  only  ^r^  =  .1846  of  a  scale  division.     If  only  one  line  of 

force  had  been  erected,  or  dissipated,  in  the  coil  C,  and  consequently 

C,  instead  of  862.4  lines  of  force,  the  galvanometer  would  have  moved 

1846 
only  5^77-7,  or  .000214  of  a  scale  division.     But  the  secondary  coil  S  on 

the  iron  ring  /  has  120  turns.     Therefore,  when  R  =  0,  one  line  of 

force  passing  through  the  coil  .Swill  throw  the  galvanometer  .000214 

division  X  120  =  .02568  scale  division.     Ans. 

When  7?'=  500,  the  total  resistance  of  the  secondary  circuit  is  increased 

from  510  ohms  to  1,010  ohms,  and  the  current  would  be  proportionally 

decreased.     (See  Art.  2480.)     Consequently,  the  scale  reading  would 

be  decreased,  and  one  line  of  force  passing  through  the  secondary  coil 

510 

5  would  cause  a  deflection  of  .02568  X  ^rn st^  =  •  01297  scale  division. 

510  +  50U 

Ans. 

When   i?'=  2,000,  the   scale   reading  per  line  of  force  =  .02568  X 

510 


510  +  2,000 


.0052  scale  division.     Ans. 


ELECTRICAL  MEASUREMENTS. 


1617 


Example. — 2.  {a)  From  the  data  and  information  following,  workout 
the  magnetomotive  force  H  in  the  primary  coil  of  the  iron  ring,  and 
the  resulting  density  of  lines  of  force  B,  using  the  step-by-step  method ; 
from  these  results  plot  a  magnetization  cttrve  on  cross-section  paper, 
showing  the  magnetic  qualities  or  susceptibility  of  the  iron,  {b)  What 
kind  of  iron  does  the  sample  seem  to  be  ? 

Data. — The  circuit  connections  are  exactly  shown  in  Fig.  991,  the 
calibrating  coil  of  the  previous  example  having  been  replaced  in  the 
primary  circuit  by  the  primary  coil  P  of  the  flat  iron  ring  /.  The 
dimensions  of  the  iron  ring  are:  5  inches  inside  diameter,  6i  inches 
outside  diameter,  and  1  inch  thick.  The  primary  coil  P  is  wound 
evenly  over  the  entire  ring  /,  and  consists  of  800  turns  of  No.  18 
insulated  wire,  affording  a  resistance  of  .8  ohm.  The  secondary  coil  is 
made  up  of  120  turns  of  No.  22  insulated  wire.  All  the  resistance  of 
the  rheostat  R ,  2,000  ohms,  is  in  circuit. 

The  data  given  and  the  results  obtained  in  the  previous  examples  are 
also  available. 

The  manner  of  performing  the  experiment  is  to  turn  in  the  whole 
resistance  of  rheostat  R  of  40  ohms,  and  then  close  the  switch  H. 
Noting  the  swing,  the  spot  of  light  gradually  settles  down  to  zero. 
The  rheostat  hand  of  R  is  suddenly  thrown  back  to  the  second  contact. 
This  cuts  out  4  ohms  resistance,  which  allows  an  additional  amount  of 
current  to  flow  through  the  circuit.  The  addition  of  this  quantity  of 
current  sets  up  additional  lines  of  force,  and  the  additional  lines  of 
force  set  up  a  current  in  the  ballistic  galvanometer  G .  The  rheostat 
is  moved  around  the  successive  steps,  and  the.  readings  noted  as 
follows: 


Resistances  of  R. 

Deflection  of 
Galvanometer  G'. 

Ohms. 

Divisions.  . 

40 

220.6 

36 

11.1 

32 

12.9 

28 

7.7 

24 

14.8 

20 

18.2 

16 

16.3 

12 

19.6 

8 

26.0 

4 

30.7 

0 

40.4 

Solution.— («)  The  calculations  should  be  made  in  tabular  form, 
for  the  sake  of  clearness.     The  following  calculations  will  have  to  be 


1618 


ELECTRICAL  MEASUREMENTS. 


made,  and  a  column  may  properly  be  assigned  for  the  result  of  each 
calculation: 

1.  The  resistance  of  the  primary  circuit. 

2.  The  current  in  the  primary  circuit. 

3.  The  magnetomotive  force  H  of  the  primary  coil  (per  inch  of 
length  of  core). 

4.  The  deflection  of  the  ballistic  galvanometer  G'  in  scale  divisions. 

5.  The  corresponding  chattge  in  the  number  of  lines  of  force  in  the 
iron  ring  /. 

6.  The  total  number  of  lines  of  force  in  the  iron  ring. 

7.  The  density  B  per  square  inch  in  the  iron. 

Column  1  is  found  by  adding  the  resistances  of  the  elements  of  the 
primary  circuit,  the  several  values  of  the  adjustable  rheostat  R  having 
been  given  in  the  example;  for  illustration,  the  first  quantity  equals 
.8-f  1.2 -f- 1.1 -f  40  =  43.1  ohms.  The  rest  are  found  in  the  same 
manner. 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

Resistance 

of 

Primary 

Circuit. 

Current 

in 
Primary 
Circuit. 

H 

Magneto- 
motive 
Force  in  Pri- 
mary Coil. 

Deflect,   of 
Galvanom- 
eter. 
Divisions. 

Change   in 
Number 
of  Lines 
of  Force. 

Total 
Number 
of  Lines 
of  Force. 

B 

Lines 
of   Force  in 

Iron,  per 
Square  Inch. 

43.1 

.2645 

37.40 

220.6 

42,420 

42,420 

56,560 

39.1 

.2916 

41.20 

11.1 

2,140 

44,560 

59,410 

35.1 

.3248 

45.90 

12.9 

2,480 

47,040 

62,720 

31.1 

.3666 

51.84 

7.7 

1,480 

48,520 

64,690 

27.1 

.4207 

59.50 

14.8 

2,850 

51,370 

68,490 

23.1 

.4935 

69.78 

13.2 

2,540 

53,910 

71,880 

19.1 

.5968 

84.40 

16.3 

3,140 

57,050 

76,070 

15.1 

.7550 

106.8 

19.6 

3,770 

60,820 

81,090 

11.1 

1.027 

145.2 

26.0 

5,000 

65,820 

87,760 

7.1 

1.606 

227.1 

30.7 

5,900 

71,720 

95,630 

3.1 

3.677 

520.0 

40.4 

7,770 

79,490 

-  105,990 

The  readings  in  column  2  are  found  by  dividing  the  total  electro- 
motive force  of  the  cells,  11.4  volts,  by  the  respective  resistances  given 
in  column  1. 

The  values  of  the  magnetomotive  force  in  column  3  can  be  calcu- 

3.192  X  a-t 


lated  from  formula  430,  H  = 


-,  where  the  number  of  turns  / 


=  800,  and  the  current  a  —  .2645,  .2916,  .3248  ampere,  etc.  ;  the  length  of 
the  magnetic  circuit  /  is  determined  from  the  dimensions  of  the  ring,  as 


ELECTRICAL  MEASUREMENTS. 


IGld 


5f  inches.     Length 


follows:  The  mean  diameter  of  the  ring  =  • — - — ^ 

/  =  5f  X  3.1416  =  18.06  inches. 

The  deflections  of  the  galvanometer,  column  4,  are  given  in  the 
example. 

The  cha)ige  in  the  number  of  lines  of  force,  that  is,  the  additional 
number  of  lines  of  force  due  to  the  increases  of  primary  current,  noted 
in  column  2,  when  the  resistance  of  the  rheostat  R'  equals  2,000  ohms,  is 
found  by  dividing  the  respective  deflections  by  .0052;  for  it  was 
shown  in  example  1,  in  the  last  answer,  that  when  R'  =  2,000  ohms, 
one  line  of  force  causes  a  deflection  of  .0052  scale  division;  therefore, 
the  number  of  lines  of  force  in  the  iron  is  the  deflection  divided  by 
.0052. 

The  total  number  of  lines  of  force,  column  6,  corresponding  to  the 
respective   magnetic  forces  tabulated  in  column  3,  are  obtained  by 
adding  the  change  in  the  number  of  lines  of  force  in  column  5  to  the 
total  number  of  lines  of  force  of  the  reading  immediately  preceding. 
-<? 

I  i2oaoor 

$ 
tioooon 

^    90000 


llOOOO 


80000 


70000 


60000 


SOOOO 


40000 


30000 


20000 


10000 


100  200  300  400  500  600 

Magneto  Motive  Force  Y\per  inch  length  Magnetic  Circuit, 

Fig.  992. 

The   lines  of  force  per  square  inch   B,   in  column  7,   are  obtained 
by  dividing  the   total  number   of   lines  of   force,    column   6,   by  the 


1620  ELECTRICAL  MEASUREMENTS. 

cross-sectional  area  of  the  iron  ring.     This  area  is  evidently  f  in.  X 
1  in.  =  .75  square  inch. 

NoTp. — The  student  is  advised  to  perform  the  computations  enu- 
merated, to  better  comprehend  the  rules  and  principles  involved. 

These  values  of  the  magnetomotive  force  H  and  the  corresponding 
density  B  of  the  lines  in  the  iron  are  now  plotted  on  a  sheet  of  cross- 
section  paper,  and  the  points  so  obtained  connected  by  a  line  forming 
the  7nagnetizatio7t  curve  of  the  piece  of  iron  under  test.  This  curve 
is  shown  in  Fig.  993. 

Solution. — {b)  Wrought  iron.  This  is  learned  by  comparing  the 
magnetization  curve  obtained  with  the  magnetization  curves  given  in 
Fig.  952. 

2487.  The  galvanometers  thus  far  described  comprise 
the  principal  forms  of  galvanometers  in  use.  The  selection 
of  any  one  instrument  for  a  test  depends  upon  its  particular 
fitness  for  that  work.  All  galvanometers,  however,  are 
merely  current  measurers,  or,  in  some  cases,  current  indi- 
cators only,  and  certain  features  of  their  use  and  certain 
apparatus  used  with  them  are  common  to  all. 


GALVANOMETER   SHUNTS. 

2488.  If  a  resistance  be  connected  in  parallel  with  a 
galvanometer  through  which  a  current  is  flowing,  the  cur- 
rent will  divide  between  the  two  branches  of 
the  circuit,  as  shown  in  Fig.  993,  inversely 
as  the  respective  resistances  of  the  circuits  ; 
and  the  galvanometer  is  said  to  be  shunted 
by  the  resistance.      (See  Art.  2320.) 

The  drop  in  volts  in  each  branch  will  be 
the  same  ;  that  is,  C^  R^  —  Cg  R^,  where 
Cg  =  current  in  galvanometer,  Cg  =  current 
in  shunt,  Rg  =  resistance  of  galvanometer, 
Rg  ■=  resistance  of  shunt.  The  total  current  (7  =  C^  +  ^g- 
The  fraction  of  the  total  current  that  passes  through  the 
galvanometer  is  found  by  the  formula 

^.  =  ^'  (454.) 


ELECTRICAL  MEASUREMENTS.  1621 

where  n  =  the  resistance  of  G  divided  by  the  resistance  of 

This    results    from    the    equations     C^   R^  —  Cg   Rg    and 

C  ^^  Cs-\-  Cg  2iS  follows :  n  =-^,  or  n  R^  =  R,j. 

Therefore,  for  CgR^  =  CgRg,  write  C^Rs  =Cg  '^  Rs,  ^^  C  = 

Cg  n ;  for  C  =  (^5+  Cg,  write  C  =  Cgn-\-  Cg,  ov  C  =  {n  -\-l)Cg. 

C 
Therefore,  Cf.  —  — — -. 

"       /z  +  1 

Thus,  by  inserting  a  known  resistance  in  parallel  with  a 
galvanometer,  also  of  known  resistance,  the  total  current 
flowing  may  be  calculated  from  the  current  flowing  in  the 
galvanometer,  as  measured  by  it.  A  resistance  arranged 
for  such  use  with  a  galvanometer  is  known  as  a  galva- 
nometer shunt. 

This  affords  a  convenient  means  of  increasing  the  range 
of  a  galvanometer,  as  by  inserting  the  proper  shunts,  cur- 
rents of  any  reasonable  multiple  of  the  normal  range  of  the 
galvanometer  may  be  measured. 

Galvanometers  are  often  furnished  by  the  makers  Avith 
shunts  of  ^,  -g-V,  and  -g-J-g-  of  the  resistance  of  the  instrument, 
which  increase  the  range  of  the  instrument  10,  100,  or  1,000 
times.  Applying  formula  454,  we  obtain  for  the  three 
differeat  shunts  the  following  currents  : 

Cc=-^  = '^- \ 

\    '       «  +  1       »  +  1  =  10/' 

/c  =  -^  = '=—^\ 

\    '       H  +  l       99  +  1  =  100/' 

(c=-^  = '=- \ 

\    "      ;/  +  1       999  +  1  =  1,000/' ■ 


The  value  of  n  -{-  1  is,  therefore,  the  amount  by  which 
any  particular  shunt  will  multiply  the  range  of  the  instru- 
ment, and  is  called  the  multiplying  power  of  that  shunt. 

In  the  foregoing  cases  the  multiplying  powers  of  the 
shunts  are  obviously  10,  100,  and  1,000,  respectively. 


1622  ELECTRICAL  MEASUREMENTS. 

2489.  To  find  the  necessary  shunt  resistance  to  make 
the  multiplying  power  of  the  shunt  any  desired  amount, 
divide  the  resistance  of  the  galvanometer  by  the  multiplying 
power    less   1;    as    the    multiplying    power  =  «-}- 1,    then, 

(;,  +  1)  _  1  =  ;,,    or  R,  =  ^. 

It  is  evident  that  introducing  the  shunt  into  the  circuit  in 
parallel  with  the  galvanometer  reduces  the  resistance  of 
that  part  of  the  circuit  (between  a  and  b.  Fig.  993).  In 
some  delicate  ineasurements  it  is  desirable  that  this  resist- 
ance be  not  altered,  and  galvanometer  shunts  are  some- 
times mounted  in  connection  with  a  second  resistance, 
known  as  a  compensating  resistance,  which  is  intro- 
duced into  the  circuit  in  series  with  the  galvanometer  and  its 
shunt.  This  resistance  is  given  such  a  value  that  its  resist- 
ance, plus  the  combined  resistance  of  the  galvanometer  and 
its  shunt  as  connected  in  parallel,  is  equal  to  the  resistance 
of  the  galvanometer  alone.  The  value  of  this  resistance  for 
any  particular  case  may  be  readily  calculated  from  the 
formulas  for  derived  circuits.      (See  Arts.  3320  to  2329.) 


EXAMPLES. 

2490.  1.  If  a  galvanometer  whose  resistance  is  21  ohms  gives  a 
deflection  of  40  with  a  current  of  2  amperes,  what  will  be  the  resistance 
of  the  shunt  that  must  be  used  to  cause  16  amperes  to  give  the  same 
deflection  ? 

Solution. — The  multiplying  power  of  this  shunt  is  evidently  8; 
therefore,  8  =  «  +  1  and  n  =  7.     R,j  =  21  and  -^^  =  3  ohms.     Ans. 

2.  What  must  be  the  value  of  a  compensating  resistance  if  used 
with  the  galvanometer  and  its  shunt  in  the  above  example  ? 

Solution. — Let  Rg  =  the  resistance  of  the  galvanometer  =  21  ohms, 
and   i?s  =  the  resistance   of  the  shunt  =  3  ohms.     By  formula  412, 

their  joint  resistance  in  parallel  is,  then,  R  =  -^-^ — ^. 

Oi    \y  Q  AQ 

Substituting  the  values  of  Rg  and  Rs,  R  =  ^. 5  =  ht  =  2.625  ohms. 

As  the  compensating  resistance  plus  the  joint  resistance  of  the 
galvanometer  and  shunt  is  equal  to  the  galvanometer  resistance,  or 
Rc  +  R  =  Rg,  substituting  the  values  gives  ^c  + 2.625  =  21,  or  Rc~ 
21  -  2. 625  =  18. 375  ohms.     Ans. 

3.  What  is  the  resistance  of  a  galvanometer  if  a  shunt  of  10  ohms 
resistance  has  a  multiplying  power  of  8  ?  Ans.  70  ohms. 


ELECTRICAL  MEASUREMENTS.  1623 

PRECISIOIV    IN    MEASUREMENTS. 

2491.  Mathematical  results  can  be  obtained  with  abso- 
lute accuracy  with  proper  attention,  but  any  measiireinents 
which  can  be  made  are  liable  to  error,  that  is,  it  can  not  be 
determined  that  the  ineasurement  is  absolutely  correct.  For 
example,  an  absolutely  rectangular  portion  of  the  top  of  a 
table  37.5  in.  long  and  20  in.  wide  has  a  surface  area  of 
absolutely  750  square  inches,  no  more  and  no  less,  but  it 
would  be  impossible  to  lay  out  a  surface  on  a  table  or  any- 
where else  that  would  be  known  to  have  a  surface  area  of 
exactly  750  square  inches. 

Results  from  a  series  of  measurements  can  not  be  expected 
to  have  a  greater  degree  of  accuracy  than  the  instruments 
with  which  such  measurements  are  made;  and,  conversely, 
it  is  unnecessary  labor  to  use  very  accurate  and  sensitive 
instruments  to  obtain  results  which  it  is  only  necessary  to 
know  approximately. 

Again,  each  of  a  series  of  measurements  should  be  made 
with  a  degree  of  precision  corresponding  to  the  effect  each 
measurement  will  have  on  the  final  result.  For  example,  if 
it  be  desired  to  find  the  cubic  inches  of  iron  in  a  bar  about 
20  feet  long  and  about  f  inch  square,  by  measuring  its  length 
and  width  and  thickness,  it  would  be  absurd  to  carefully 
measure  the  length  to  eighths  of  an  inch  with  a  graduated 
scale,  and  then  to  estimate  the  width  and  thickness  by  using 
the  end  joint  of  the  thumb  as  an  inch  and  estimating  by  the 
eye  the  fraction  of  that  distance  that  would  equal  the  width 
or  thickness  of  the  bar. 

In  making  delicate  tests  that  require  a  high  degree  of  ac- 
curacy, the  subject  should  be  carefully  studied,  and  pre- 
cautions taken  to  remove  as  far  as  possible  any  source  of 
error;  the  reading  should  be  repeated  several  times,  and,  if 
possible,  repeated  with  different  methods  and  apparatus. 
Even  then  the  best  that  can  be  said  is  that  the  results  are  as 
nearly  accurate  as  the  apparatus  will  allow,  to  the  best  of 
one's  judgment. 

So,  in  making  measurements,  electrical  or  otherwise,  care 
should  be  taken  to  make  the  apparatus,  methods  of  using  it. 


1624  ELECTRICAL  MEASUREMENTS. 

and  the  necessary  calculations  as  accurate  as  the  required 
degree  of  precision  of  the  final  result  requires.  At  the  same 
time  unnecessary  labor  in  making  one  part  of  the  work  pre- 
cise beyond  a  point  where  the  unavoidable  errors  in  another 
part  would  neutralize  such  precision  should  be  avoided. 

2-492.  This  leads  to  the  consideration  of  how  many 
significant  figures  to  retain  in  the  readings,  calculations,  and 
results  to  obtain  results  within  the  accuracy  of  the  instru- 
ments used.  By  significant  figures  is  meant  the  number 
of  digits,  with  the  exception  of  the  zeros  used  to  indicate  the 
position  of  the  decimal  point. 

For  example,  20467,  28.321,  and  .00010569  would  each 
have  five  significant  figures.  If  it  were  necessary  to  use  but 
four  significant  figures,  these  values  would  be  written  20470, 
28.32,  or  .0001057;  that  is,  if  the  figure  dropped  be  5  or 
greater,  the  next  figure  to  the  left  is  increased  1 ;  if  less  than 
5,  the  figure  to  the  left  is  unchanged.  Zeros  are  some- 
times significant  figures,  as  in  the  example,  25  X  4  =  100, 
which  has  three  significant  figures  in  the  answer,  100,  as  the 
example  has  been  carried  out  far  enough  to  show  that  the 
value  of  units  and  tens  is  0  in  each  case.  In  the  previous 
example  where  four  significant  figures  are  required,  the  num- 
ber 20470  indicates  that  the  actual  value  of  the  last  figure  0 
is  known  to  be  within  5  units  either  way  from  0.  Whereas, 
if  five  significant  figures  were  required,  20470  would  indicate 
that  the  last  number  was  known  to  be  within  ,5  unit  either 
way  from  0. 

The  requirements  of  the  calculations  and  results  of  obser- 
vations in  this  respect  are  as  follows: 

(«)  If  any  one  of  the  measurements  can  not  be  deter- 
mined within  1^,  four  significant  figures  retained  in  any 
reading,  calculation,  or  result  will  give  an  answer  correct 
within  the  limits  of  precision  of  the  measurements. 

{Jj)  If  any  one  of  the  measurements  can  not  be  deter- 
mined within  less  than  0.1^,  but  can  be  within  1^,  five 
significant  figures  are  required,  and  {c)  if  not  within  0.01^, 
but  within  0.1^,  six  significant  figures  are  required. 


ELECTRICAL  MEASUREMENTS.  1625 

The  degree  of  precision  of  the  various  instruments  used 
in  making  electrical  measurements  can  be  obtained  either 
from  careful  calibration  or  from  the  maker's  guarantee,  and 
results  obtained  from  such  instruments  may  be  calculated 
with  the  allowable  degree  of  accuracy  by  observing  the  re- 
quirements given. 

ELECTROCHEMICAL  MEASUREMENTS. 

2493.  The  decomposition  of  liquids  by  the  electric  cur- 
rent affords  a  means  of  measuring  the  current  that  requires 
but  little  apparatus  and  gives  very  precise  results.  This 
method  is  chiefly  used  for  determining  galvanometer  con- 
stants, as  it  is  not  usually  well  suited  for  the  measurement 
of  commercial  currents,  that  is,  currents  used  for  light- 
ing, power,  etc. 

The  following  constants  for  the  decomposition  of  water 
have  been  accurately  determined.  A  current  of  1  ampere 
flowing  for  1  second  will  decompose  .00009324  gram 
(.0014388  grain)  of  water.  The  gas  resulting  from  this  de- 
composition is  a  mixture  composed  of  .00001036  gram  of 
hydrogen  and  .00008288  gram  of  oxygen;  so,  by  measuring 
the  amount  of  water  decomposed  by  a  current  in  a  given 
time,  either  by  measuring  the  loss  of  weight  of  the  water  or 
by  measuring  the  volume  of  either  or  both  gases  given  off, 
the  value  of  the  current  may  be  calculated.  The  latter 
method  is  called  the  volume  method.  Since  corrections  must 
be  made  for  temperature,  pressure,  etc.,  in  determining  by 
their  volume  the  weight  of  the  gases  collected,  this  method 
involves  considerable  labor  and  time.  It  is  usually  simpler 
to  use  the  first  mentioned,  or  zueight  metJiod. 

2494.  In  this  method  the  gases  resulting  from  the  de- 
composition of  the  water  are  allowed  to  escape  into  the  air. 
If  they  were  allowed  to  pass  off  directly  from  the  surface  of 
the  water,  considerable  water  vapor  would  pass  off  with 
them,  and  the  loss  of  weight  of  the  water  would  not  be 
a  true  measure  of   the  current   flowing;  these   gases   are, 


1626 


ELECTRICAL  MEASUREMENTS. 


therefore,  made  to  pass  through  a  certain  apparatus  known 
as  a  desiccator,  which  consists  merely  of  a  glass  tube, 
loosely  filled  with  some  substance  which  will  absorb  the 
water  vapor  while  allowing  the  gases  to  escape  unchanged. 
The  whole  apparatus,  including  desiccator  and  water,  should 
be  weighed,  and  the  difference  between  the  weight  before 
and  after  the  passage  of  the  current  will  represent  the 
value  of  the  current. 

Fig.  994  shows  two  forms  of  apparatus  for  this  method  of 

measuring  current.     The  tube 

! r        T    contains    the     liquid    and 

the  (platinum)  electrodes, 
which  pass  through  a  cork 
'*«  which  has  been  boiled  in  par- 
affin. The  tube  t  is  the  des- 
iccator, and  is  loosely  filled 
with  asbestos  soaked  in  sulphu- 
ric acid.  The  small  tube  in 
the  end  of  the  tube  /,  through 
which  the  gases  pass  off,  should 
be  closed  with  a  paraffined 
cork  c  previous  to  and  just  af- 
ter the  passage  of  the  current, 
to  prevent  the  acid  in  the  tube 
/  absorbing  moisture  from  the 
air,  which  would  introduce  an 
error. 

The  second  form  of  appa- 
ratus illustrated  is  more  diffi- 
cult to  make.  The  joints  at 
s^  and  s^  are  ground  to  fit, 
and  wires  to  the  electrodes  are  sealed  into  the  sides  of  the 
tube  T. 

As  pure  water  has  an  extremely  high  resistance  (one  au- 
thority gives  7  megohms  per  cubic  centimeter),  it  is  neces- 
sary to  add  some  substance  to  increase  its  conductivity. 
For  these  tests  sulphuric  acid  is  used;  a  small  proportion  of 
acid  is  sufficient. 


Fig.  994. 


ELECTRICAL  MEASUREMENTS.  1627 

2495.  To  measure  current  with  this  apparatus,  the 
tube  T  should  be  filled  with  acidulated  water,  and  the  tube  t 
with  asbestos  soaked  in  sulphuric  acid.  With  the  cork  c  in 
place,  carefully  weigh  the  whole  apparatus.  Then  join  the 
terminals  of  the  apparatus  to  the  battery  from  which  the 
current  is  to  be  taken,  and  removing  the  cork  r,  note  the 
exact  time  at  which  the  final  connection  is  made  to  the  bat- 
tery. It  is  better  to  use  some  form  of  switch  for  closing  the 
circuit  after  all  connections  have  been  made.  After  allow- 
ing the  current  to  pass  until  sufficient  water  has  been 
decomposed,  break  the  circuit,  noting  again  the  exact 
instant  the  current  ceases  to  flow,  replace  the  cork  c  and 
reweigh  the  apparatus. 

To  find  the  strength  of  the  current  that  has  been  passing 
in  amperes: 

Let  Wj  =  the  original  weight  of  apparatus; 

w^  =  the  weight  after  the  current  has  passed ; 
/  =  time  in  seconds  during  which  the  current  flows; 
C  =  strength  of  current  in  amperes. 

Then,  if  the  weights  are  taken  in  grains, 

.00009324/  l^»»-; 

If  the  weights  are  In  grainSy 

.0014388/-  ^4r>0.; 

Rule. —  To  determine  the  strengtJi  of  a  ciirrent  by  decom- 
position of  water y  subtract  from  the  original  zveight  of  the 
apparatus  its  weight  after  the  current  has  passed  tJirough  ; 
divide  this  result,  expressed  in  grams  or  grains,  by  the  length 
of  time  the  current  ivas  passing,  in  seconds,  multiplied  by  the 
number  of  grams  or  grains  of  water  which  can  be  decomposed 
by  1  ampere  in  1  second. 

Example. — The  original  weight  of  the  apparatus  was  980.5  grams  ; 
the  current  was  passed  through  for  38  minutes,  and  the  weight  was 
then  found  to  be  979.6  grams;  what  was  the  strength  of  the  current  in 
amperes  ? 


1628  ELECTRICAL  MEASUREMENTS. 

Solution. — In  this  example,  Wi  =  980.5  grams  ;  w-^  =  979.6  grams 
88  minutes  =  2,280  seconds  =  /.     Then,  by  formula  455, 

980.5-979.6  .9  .  _„„  ,  . 

^=.00009324X2,280  =  :2i25872  =  ^•'''+  ^"^P^^^^"     ^"^- 

It  will  now  be  readily  seen  that  if  a  galvanometer  be  con- 
nected in  series  with  the  apparatus  for  decomposing  the 
water,  and  the  deflection  noted,  its  galvanometer  constant 
may  be  easily  calculated. 

EXAMPLES  FOR  PRACTICE. 

1.  If  the  loss  in  weight  of  apparatus  be  3.462  grains  after  a  current 
has  passed  through  for  40  minutes,  how  many  amperes  have  been 
passing  ?  Ans.  1.0025  amperes. 

2.  If  .756  ampere  is  passed  through  the  apparatus  for  1  hour,  what 
will  be  the  loss  of  weight  of  the  apparatus  {a)  in  grams  ?  {b)  in  grains  ? 

Ans.    i(-)-2537+. 
({b)  3.9158 -h. 

Note. — In  decomposing  water,  a  battery  of  sufficient  number  of 
cells  to  give  about  3  volts  should  be  used.  The  cells  should  give 
a  constant  current. 

2496.  If  a  solution  of  copper  sulphate  (blue  vitriol)  be 
used  instead  of  acidulated  water,  the  decomposition  of  the 
liquid  by  the  current  will  cause  a  deposit  of  copper  on 
the  negative  plate.  The  weight  of  copper  deposited  in'  a 
given  time  is  proportional  to  the  current  flowing,  and  1 
ampere  will  deposit  .0003286  gram  of  copper  in  1  second. 
Moderate  variations  in  the  proportions  of  copper  sulphate  in 
the  solution  or  the  temperature  do  not  affect  the  result 
appreciably.  The  above  figure  is  given  for  a  half  saturated 
solution  of  copper  sulphate  [that  is,  about  1  part  (by  weight) 
of  copper  sulphate  to  5  parts  of  water]  at  a  temperature  of 
73°  F.  A  reduction  of  temperature  to  54°  F.  would  not 
alter  the  figure  given  by  more  than  .03^, 

In  making  measurements  of  the  amount  of  copper  depos- 
ited, electrodes  of  copper  should  be  used,  of  such  size  that 
there  shall  be  from  8  to  15  square  inches  of  surface  to  be 
deposited  upon  for  each  ampere  of  current. 

When  the  copper  is  deposited  from  the  copper  sulphate 
solution,  sulphuric  acid  is  set  free,  which  dissolves  a  portion 


ELECTRICAL  MEASUREMENTS.  1629 

oi  the  positive  plate,  forming  copper  sulphate,  thus  keeping 
the  amount  of  copper  sulphate  in  solution  practically  con- 
stant. The  positive  plate  does  not  lose  in  weight  in  direct 
proportion  to  the  current  passing,  so  in  measurements  of 
this  description  the  gain  in  weight  of  the  negative  plate 
only  is  measured. 

2497.  Apparatus  prepared  according  to  the  following 
description  will  afford  a  means  of  measuring  the  current, 
which  requires  even  less  apparatus  than  the  weight  method 
of  water  decomposition,  but  the  precautions  therein  noted 
should  be  taken  to  insure  reliable  results. 

Trough. — The  vessel  or  trough  used  should  be  of  wood 
or  other  insulating  material,  of  sufficient  size  to  allow  the 
square  part  of  the  plates  to  hang  entirely  below  the  surface 
of  the  liquid. 

2498.  Plates. — It  would  be  best  to  use  three  plates, 
one  negative  or  £^am  plate,  suspended  between  two  positive 
or  loss  plates,  which  should  be  of  the  same  shape  and  mate- 
rial as  the  gain  plate,  but  somewhat  smaller  and  thicker 
The  gain  plate  should  be  of  very  thin  copper,  so  that  its 
gain  in  weight  will  be  enough  to  make  considerable  differ- 
ence between  its  weights  before  and  after  the  test. 

The  plates  should  be  cut  approximately  square  and  the 
corners  clipped  off.  It  is  rather  better  to  make  them  circu- 
lar, but  this  form  is  often  not  as  convenient  to  prepare,  and 
is  not  at  all  necessary.  From  one  side  of  the  plate  a 
narrow  strip  should  be  left  projecting,  long  enough  to  bend 
into  a  hook  by  which  to  hang  the  plate  on  the  scales  or  in 
the  liquid. 

Three  pieces  of  heavy  bare  copper  wire  or  rod  should  be 
provided,  long  enough  to  reach  across  the  top  of  the  trough ; 
on  resting  these  on  the  edges  of  the  trough  a  short  distance 
apart,  the  electrodes  may  be  readily  hung  from  them  and 
the  necessary  connections  made  to  them  from  the  battery. 

The  positive  plates  should  be  rubbed  bright  on  both 
sides  with  fine  sandpaper.     The  negative  plate  should  be 


1630 


ELECTRICAL  MEASUREMENTS. 


carefully  rubbed  smooth  and  bright  with  very  fine  sandpaper 
or  emery,  taking  great  care  not  to  touch  the  part  of  the 
bright  surface  that  will  be  below  the  surface  of  the  liquid 
with  the  bare  fingers  or  any  greasy  substance.  A  piece  of 
clean  paper  or  cloth  should  be  used  to  handle  the  plate  with. 
After  carefully  brightening  the  plate,  it  should  be  washed  and 
dried  carefully  several  times,  and  then  accurately  weighed. 
This  preparation  of  the  gain  plate  should  not  be  made 
until  all  the  rest  of  the  apparatus  is  ready,  as  a  long  expo- 
sure to  the  air  will  oxidize  the  bright  surface  of  the  copper. 

2499.  Liquid. — Make  the  liquid  by  dissolving  1  part 
(by  weight)  of  crystals  of  copper  sulphate  in  5  parts  (by 
weight)  of  water,  and  adding  about  1  per  cent,  of  strong 
sulphuric  acid.  (One  per  cent,  is  about  3  teaspoonfuls 
to  the  quart.)  This  excess  of  acid  serves  to  dissolve  such 
impurities  as  may  exist  in  the  copper  sulphate. 

A  conducting  liquid  thus  prepared  for  electrolysis  or  for 
use  in  a  battery  is  known  as  an  electrolyte.  (See  Art. 
2238.)  Other  salts  of  metals  in  solution  besides  the  above 
may  be  used  as  the  electrolyte,  with  corresponding  metals 
as  electrodes. 

2500.  Battery  and  Connections. — A  battery  of 
two  cells  in  series  will  be  sufficient  if  small  currents  are 

desired.  Cells  should  be  used  giving 
approximately  a  constant  current.  If 
constant-current  batteries  are  not  avail- 
able, use  three  or  four  cells  of  some 
other  type,  and  insert  a  resistance 
which  may  be  varied  to  keep  the  cur- 
rent constant.  The  various  forms  of 
cells  will  be  described  later.  Connec- 
tions should  be  made  by  means  of 
insulated  wires,  as  shown  in  Fig. 
995,  where  5  =  switch  for  making  and 
breaking  the  circuit  ;  B  =  battery; 
keeping    the    current    constant;     G  = 


Fig.  995. 


R  =  resistance 
galvanometer; 


for 


7"=  trough   containing   plates    and   liquid-, 


ELECTRICAL  MEASUREMENTS.  1631 

W,  IF,  JV  =  copper  wires  across  top  of  trough  from  which 
plates  are  hung. 

2501.  After  preparing  the  solution  and  setting  up  the 
apparatus,  the  positive  plates  should  be  hung  in  place,  then 
the  negative  plate  should  be  prepared  and  weighed;  as  soon 
as  possible  hang  the  negative  plate  in  place;  put  in  sufficient 
liquid  to  completely  cover  the  plates;  then,  close  the  switch, 
noting  the  exact  instant  when  the  circuit  is  made.  The  de- 
flection of  the  galvanometer  needle  should  be  noted  from 
time  to  time,  and  any  change  in  the  deflection  corrected  by 
changing  the  resistance  R.  After  sufficient  time  has 
elapsed,  open  the  switch,  again  noting  the  exact  time. 

As  soon  as  possible,  take  out  the  negative  plate,  wash  and 
dry  it  carefully  several  times,  and  accuratel}^  weigh  it. 
Then,  find  the  amperes  that  have  been  flowing  by  the  fol- 
lowing formulas : 

Let  Wj  =  the  original  weight  of  gain  plate ; 

w^  =  the  weight  after  the  current  has  passed; 
it  =  time  in  seconds  during  which  the  current  flows; 
C  =  strength  of  current  in  amperes. 

Then,  if  the  weights  are  in  grams, 

~  .0003286  f  ^^^^--^ 

If  the  weights  are  in  grains, 

.005068/-  14»»-; 

Rule. — In  order  to  determine  the  strength  of  ciirre7if  by 
measurement  of  copper  deposited,  subtract  the  original  zveiglit 
of  the  gain  plate,  in  grams,  from  the  weight  as  found  after 
the  experiment;  divide  this  result  by  the  length  of  time  the 
current  was  flowing  in  seconds  utultiplied  by  the  number  of 
grams  of  copper  which  can  be  deposited  by  1  ampere  in  1  second. 

After  finding  the  current  which  has  been  passing,  the 
galvanometer  constant  can  be  found  from  formulas  448 
and  450. 


1632  ELECTRICAL  MEASUREMENTS. 

Example. — The  negative  plate  io  a  sheet  of  copper  about  2^  in. 
square  and  about -jV  in.  thick.  After  cleaning,  it  weighs  29.62  grams. 
The  current  being  allowed  to  pass  for  75  minutes,  the  plate  weighs 
31.33  grams.  A  tangent  galvanometer  in  circuit  gave  a  deflection  of 
42°.  (a)  How  many  amperes  were  passing,  and  {i>)  what  was  the  gal- 
vanometer constant  ? 

Solution. — (a)  In  this  example,  Wi=:  29.62  grams;  'Z£'a=  31.33  grams; 
/f  =  75  X  60  =  4,500  seconds.     Then,  by  formula  457,  the  current 

31.33-  29.62         ,  .^„.  . 

^  =  .0003286X4.500  =  ^'^^'^  ^"^P"^"^'     ^'^^ 

{d)  Use  formula  450. 

€■=  K  tan  m*. 
Tan  43°  =  .9004. 

Then, z  =  K\ 

tan  771 

Note. — The  weight  of  copper  deposited  per  ampere  per  second  may 
be  taken  in  grains  (Troy)  instead  of  grams,  and  the  result  worked  out 
in  the  same  way.     1  gram  =  15.432  grains  (Troy). 

Example. — Change  the  weights  in  the  above  example  to  grains  and 
work  out  the  results. 

MEASUREMENT  OF  POTENTIAL. 
2502.  If  two  points  between  which  a  difference  of 
potential  exists  are  connected  together  by  a  conductor,  a 
current  will  flow  from  one  to  the  other,  its  value  depending 
on  the  resistance  of  the  conductor  and  the  difference  of 
potential  between  the  two  points. 

If  this  conductor  be  the  coil  of  a  galvanometer,  it  is 
obvious  that  the  divisions  on  the  scale   may  be  marked  to 

read    volts     instead    of 
amperes. 

In  Fig,  996  a  current 

flows  from  the  battery 

B   through   the    resist- 

"5^  ance    abed.     There 

FIG.  996.  will,     therefore,     be    a 

certain  fall  of  potential  along  abed,  and  it  may  be  desired 

to  measure  the  difference  of  potential  between  b  and  c. 


ELECTRICAL  MEASUREMENTS.  1633 

2503.  If  a  galvanometer  whose  resistance  is  approxi- 
mately that  of  the  part  of  the  circuit  b  c  x?,  connected  to 
the  points  b  and  c,  the  current  flowing  from  a  to  b  will 
divide  at  b,  and  a  part  flow  through  the  galvanometer  G. 
The  whole  current  will  again  flow  from  c  to  d.  If  the  resist- 
ance of  the  galvanometer  is  known,  the  current  flowing 
through  it,  as  measured  by  the  deflection  of  the  needle,  is 
also  a  measure  of  the  difference  of  potential  between  b  and  c, 
but  this  difference  of  potential  is  not  the  same  as  it  was 
before  the  galvanometer  was  connected. 

The  galvanometer  being  placed  in  parallel  with  a  part  of 
the  circuit  reduces  the  total  resistance  of  the  circuits,  and 
as  the  distribution  of  resistance  between  a  and  d?  is  changed, 
the  distribution  of  the  fall  of  potential  will  also  be  changed. 

In  order,  therefore,  to  measure  the  difference  of  potential 
between  b  and  c,  the  instrument  used  should  be  so  con- 
structed that  it  will  not  measurably  alter  the  conditions  of 
the  circuit.  If  the  galvanometer  G  in  Fig.  996  have  a  very 
high  resistance  as  compared  with  b  c^  so  that  the  current 
passing  through  it  will  be  a  very  small  percentage  of  the 
total  current  in  the  circuit,  the  conditions  will  not  be  altered 
sufficiently  to  introduce  any  serious  error. 

2504.  When  a  difference  of  potential  exists  between 
two  points  between  which  no  current  is  flowing,  as  a  battery 
with  no  external  circuit  made,  it  is  usually  the  case  that 
any  considerable  current  flowing  will  reduce  this  difference 
of  potential,  owing  to  the  internal  resistance  of  the  battery 
or  other  generator  of  the  E.  M.  F. 

To  measure  this  difference  of  potential  again  requires  a 
galvanometer  of  such  resistance  that  a  very  small  current 
will  flow  through  it,  in  order  that  the  conditions  of  the  cir- 
cuit shall  not  be  sensibly  changed;  so  that  commercial 
measuring  instruments  that  are  constructed  on  the  galva- 
nometer principle  are  divided  into  two  classes : 

1.  Instruments  of  low  resistance,  so  arranged  that  a  con- 
siderable current  is  required  to  give  readable  deflections, 
usually  with  the  scales  so  marked  as  to  give  the  deflicction 


1G34 


ELECTRICAL  MEASUREMENTS. 


of  the  needle  the  proper  value  in  amperes  of  the  current 
passing  through  the  instrument.  These  are  called  am- 
pere-meters, or  more  briefly  ammeters. 

2.  Instruments  of  high  resistance,  so  arranged  that  very 
small  currents  will  give  readable  deflections,  and  with  the 
scales  usually  so  marked  as  to  give  the  deflection  of  the 
needle  the  proper  value  in  volts  of  the  difference  in  poten- 
tial between  the  points  to  which  the  instrument  is  connected. 
Such  instruments  are  called  voltmeters. 


2505.  Fig.  997  illustrates  a  method  of  measuring  dif- 
ferences of  potential,   in  which   the   principle  of   operation 

necessitates  that  no  cur- 
rent be  flowing  through 
the  galvanometer  G.  In 
the  figure,  abed  is  a  re- 
sistance through  which  a 
current  is  flowing,  sup- 
plied by  the  battery  B.  It 
is  desired  to  measure  the 
difference  of  potential  be- 

+  lilitililTlili ^-  tween  Z*  and  <r,     5  is  a  bat- 

FiG.  997.  tery  of  standard  cells,  the 

E.  M.  F.  of  which  is  known,  arranged  so  that  one   or  more 
of  the  cells  in  series  may  be  used. 

If  the  negative  pole  of  the  battery  5  be  connected  to  the 
same  end  oi  b  c  that  the  negative  pole  of  B  is  connected, 
and  the  positive  pole  of  S  to  the  other  end  of  be,  through 
the  galvanometer  G,  it  will  be  seen  that,  if  the  battery  5 
had  no  E.  M.  F.  of  its  own,  the  difference  of  potential 
between  b  and  c  would  tend  to  drive  a  current  through  5 
from  b  to  r,  which  would  be  indicated  by  the  galvanometer. 
5"  has  an  E.  M.  F.,  however,  which,  from  the  way  it  is  con- 
nected, opposes  the  passage  of  such  a  current,  and  if  the 
E.  M.  F.  of  vS  exactly  equals  the  drop  in  volts  between  b 
and  r,  no  current  will  flow  through  S.  To  measure  the 
difference  of  potential  between  b  and  c,  it  only  remains  to 
adjust  the  number  of  cells  in  5  until  the  galvanooaeter  G 


ELECTRICAL  MEASUREMENTS. 


1635 


indicates  no  deflection ;  then,  multiplying  the  E.  M.  F.  of 
each  cell  in  vS  by  the  number  used  will  give  the  drop  in 
volts  between  b  and  c. 

As  no  current  flows  through  the  galvanometer,  it  may  be 
large  or  small,  of  high  or  low  resistance,  as  long  as  it  is 
sensitive  to  sraall  currents.  Consequently,  various  current 
strengths  and  differences  of  potential  may  with  this  method 
(called  the  zero  method)  be  measured  with  a  single  gal- 
vanometer 


i 


I- 


^--♦^V\A/VW\AAA;y\AA»-- 


MEASUREMENT  OF  RESISTANCE. 
2506.  The  resistance  of  a  conducting  body  may  be 
measured  in  a  variety  of  ways.  One  of  the  most  common 
is  the  fall  of  potential  method,  which  consists  of  passing 
a  current  through  the  unknown  resistance  and  measuring 
the  amperes  flowing  and 
the  drop  in  volts  through 
the  resistance.  The  resist- 
ance is  calculated  from 
Ohm's  law.  Fig.  998  shows 
the  arrangement  of  the  ap- 
paratus, -a  be d  h  z.  resist- 
ance of  which  it  is  desired 
to  know  the  resistance  b  c.  f^°-  ^9^- 

A  current  from  the  battery  B  flows  through  the  ammeter 
A  M  and  the  resistance.  The  drop  in  volts  from  b  to  c  \'s> 
measured  by  the  voltmeter  V  M. 

Example. — 1.  If  the  current  flowing  from  a  to  d  he  2.2  amperes, 
and  the  drop  from  b  to  c  he  ^.25  volts,  what  is  the  resistance  of  the 
part  of  the  circuit  bcl 

E_ 

C 


V.M. 


Solution. — By  formula  41 0,  7? 
6.25 


£•=6.25.     (7  =  2.2.     i?  = 


3.2 


=  2.841  ohms.     Ans. 


2.     If  the  current  be  found  to  be  21.25  amperes,   and  the  drop  in 
potential  4.6  volts,  what  is  the  resistance  ?  Ans.  .2165  ohm. 

2507.     This  method  of   measuring   resistance  is  often 
not  convenient,  and  many  times  impossible  to  use.     Another 


1636 


ELECTRICAL  MEASUREMENTS. 


method  is  to  compare  the  unknown  resistance  with  one  or 
more  known  resistances  in  several  ways.  It  may  be  done 
by  connecting  a  known  and  the  unknown  resistance  in 
series,  and,  on  sending  a  current  through  the  two,  measure 

ing  the  drop  in  volts  across 
each.  The  resistances  will  be 
directly  proportional  to  the 
fall  of  potential,  and  the 
current  need  not  be  meas- 
ured. 

In  Fig.  999,  B  is  the  bat- 
tery,  the  current  from  which 
flows  through  the  known  resistance  a  b  and  the  unknown 
resistance  b  c.  Voltmeters  V  M  and  K,  J/,  measure  the 
fall  of  potential  across  each.  The  same  voltmeter  might 
readily  be  used  for  both  readings. 

Example. — 1.  If  the  resistance  ab\s  known  to  be  2  ohms,  and  the 
drops  as  measured  by  V M  and  Vi  Mi  are  4.25  volts  in  ad  and  6.13 
volts  in  b c,  what  is  the  resistance  oi  b cl 

Solution. — As  the  resistances  are  directly  proportional  to  the  drops 
of  potential, 


Fig.  999. 


4.25 


or, 


2x6.12 
4.25 


6.12 
12.24 


4.25 


ohms.     Ans. 


Example. — 2.  If  the  drop  through  the  known  resistance  is  6.28  volts 
and  through  the  unknown  2.25,  what  is  the  unknown  resistance  if  the 
known  is  3.5  ohms  ?  Ans.  1.254  ohms. 

2508.  Another  way  to  attain  the  same  result  would  be 
to  connect  the  known  and  the  unknown  resistance  in  parallel, 
and  measure  the  current 
in  each.  The  currents 
would  be  in  inverse  pro- 
portion to  the  resistances. 
In  Fig.  1000  the  current 
from  the  battery  B  di- 
vides at  .r,  a  part  flowing 
through  the  known  resist- 
ance a  b  and  the  balance 
through     the      unknown  Fig.  looo. 


ELECTRICAL  MEASUREMENTS.  1637 

resistance  c d.     Ammeter  A  M  measures  the  current  \n  ah 
and  ammeter  A^  M^  measures  the  current  in  c  d. 

It  is  to  be  noted  that  the  ammeters  and  their  connecting 
wires  should  be  of  such  low  resistance  as  not  to  add  mate- 
rially to  the  resistance  of  either  branch  of  the  circuit. 

Example. — If  ammeter  AM  indicates  3.6  amperes  and  ammeter 
Ax  Mx  indicates  4.3  amperes,  what  is. the  resistance  oi  c  d  \i  ab  is  10.5 
ohms  ? 

Solution. — As  the  currents  are  inversely  proportional  to  the  resist- 
ances, 

4.2  :  3.6  ::  10.5  :  x\ 

3.6X10.5      37.80      ^    ,  . 

or  x  = ^ —  =  -^  =  9  ohms.     Ans. 

2509.  In  Fig.  1000  the  drop  along  c  d  must  be  the  same 
as  that  along^  d  (neglecting  the  ammeter  resistances).  If 
any  point  in  c  d  he  selected,  a  point  in  a  if  can  be  found  that 
will  have  the  same  difference  of  potential  between  it  and  x 
that  the  point  in  c  d  has. 

If  a  galvanometer  is  connected  across  from  the  point  in  ^  ^ 
to  the  point  in  a  d,  no  current  will  flow  through  it,  as  there 
is  no  difference  of  potential  be- 
tween the  points.  Fig.  1001  rep- 
resents this  condition. 

It  is  obvious  that  the  resistance 
from  a  to  7Z  must  be  the  same 
proportion  of  the  total  resistance 
a  b  that  the  resistance  from  c  to 
m  is  of  c  d,  in  order  that  the  drop 
in  a  n  shall  be  the  same  as  in  c  in. 
If  the  point  n  be  moved  to  any 
point  in  a  b,  the  point  m  must  be 
correspondingly  moved  on  c  d,  in  order  that  there  may 
be  no  current  flowing  though  G,  and  that  the  proportion 
a  11  :  a  b  \\  c  111  :  c  d  may  still  hold  good. 

It  is  also  evident  that  the  same  proportion  holds  good  for 
K  b  and  in  d  \  i.  e.^  n  b  '.  a  b  w  in  d  \  c  d. 

From  the  above  proportions, 

an  '.  c  in  ::  a  b  :  c  d,  and  n  b  :  m  d  w  a  b  :  c  d. 

Therefore,  an  :  c  in  v.  n  b  :  in  d. 


1638 


ELECTRICAL  MEASUREMENTS. 


That  is,  the  resistance  of  a  n  is  to  the  resistance  of  c  in  as 
the  resistance  of  n  b  is  to  the  resistance  of  in  d. 

From  this  proportion,  it  is  evident  that  if  a  ii,  c  in,  and  in  d 
be  known,  the  resistance  of  ii  b  may  be  readily  calculated. 

This  affords  a  ready  means  for  measuring  resistance, 
which,  as  will  be  shown,  is  very  flexible  and  universally 
applicable. 

25  lO.  In  Fig.  1002,  M,  N,  and  /'are  three  known  resist- 
ances, which  may  be  varied  by  known  amounts.  An  un- 
known resistance  X  is  connected  to  c  and  b,  completing  the 

c 


branch  a  c  b  oi  the  circuit  from  a  to  b.  Through  this  circuit 
a  current  flows  from  the  battery  B.  Any  one  of  the  three 
resistances  M,  N,  and  P  may  be  adjusted  until  the  galva- 
nometer G  indicates  that  the  points  c  and  d  are  at  the  same 
potential;  then,  from  the  proportion  given  in  Art.  2509, 
M:N'.:X:P. 

It  is  obvious  that  if  M  be  equal  to  N,  Jf  will  be  equal  to  P, 
while  if  X  be  a  very  high  or  very  low  resistance  it  may  be 
measured  equally  well  by  changing  the  ratio  oiMtoN.      In 

any  case, 

M 


X^j^xR 


(459.) 


This  method  of  measuring  resistance  is  known  as  the 
Wlieatstone  bridge  method,  and  the  instrument  used  is 
called  a  Wheatstone  bridge,  or,  more  commonly,  a 
bridge. 


ELECTRICAL  MEASUREMENTS. 


1639 


In  practice,  the  arms  J/,  N,  and  P  of  the  bridge  are  made 
up  of  a  number  of  carefully  prepared  resistance  coils,  ac- 
curately adjusted  to  different  resistances,  fixed  in  a  box,  on 
the  top  of  which  are  arranged  blocks  of  brass,  which  form  the 
terminals  of  the  coils.  The  brass  blocks  are  so  situated  that 
by  inserting  a  metallic  plug  between  any  two  of  them  the 
corresponding  resistance  coil  is  cut  out,  or  sJwrt-circiiited ; 
that  is,  the  current  passes  from  block  to  block  through  the 
plug  instead  of  going  through  the  coil,  as  this  path  offers 
practically  no  resistance  to  the  current.  In  this  way  the 
resistance  of  the  arms  of  the  bridge  is  changed. 

Fig.  1003  shows  a  section  of  a  box  of  coils  showing  the 
brass  blocks  and  the  method  of  cutting  out  the  coils,  a,  b,  c, 
</,  ^,  y,  and  ^  are  the  brass  blocks,  to  which  are  connected  the 


4      3      2 

Fig.  1003. 

coils  1,  ^,  3y  4-,  5^  and  6.     The  brass  plug  P  is  made  to  fit 
tightly  between  the  blocks. 

The  current  from  the  battery  is  not  allowed  to  flow  con- 
tinuously through  the  resistance  coils,  which  might  introduce 
errors  owing  to  the  heating  effect  of  the  current,  but  the 
battery  circuit  and  galvanometer  circuit  are  each  provided 
with  a  key.  On  pressing  the  battery  circuit  key,  the  current 
passes  through  the  bridge,  and  on  then  pressing  the  galva- 
nometer key,  it  is  seen,  from  the  motion  or  lack  of  motion 
of  the  needle,  if  the  proportion  of  resistance  is  correct.  It 
is  usual  to  make  the  arms  J/ and  N  oi  comparatively  few 
coils,  with  ratios  of  10;  for  example,  1,  10,  100,  and  1,000 
ohms.  By  cutting  out,  for  instance,  all  but  the  1-ohm  coil 
in  one  arm,  and  leaving  all  the  coils  in  the  other,  the  ratio 
of  J/ to  iV  is  1,111  to  1,  or  1  to  1,111,  as  the  case  may  be;  so 
that  an  instrument  thus  arranged  would  nie9,sure  resistances 


1640 


ELECTRICAL-  MEASUREMENTS. 


TT^TT 


of 


varying  from  1,111    times  the  largest  value  of  P  to 
the  smallest  value  of  P. 

For  bridge  measurements  requiring  a  considerable  degree 
of  accuracy,  it  is  best  to  use  a  sensitive  reflecting  galva- 
nometer, which  will  respond  to  very  slight  differences  in 
potential  between  c  and  d  (in  Fig.  1002). 

251 1 .  In  Fig.  1004  is  shown  an  arrangement  of  a  bridge 
in  which  H  G  corresponds  to  arm  M  (in  Fig.  1002),  E  F  to 


Galv. 


FIG.  1004. 

arm  N,  A  B  C  D  to  arm  P,  and  x  to  the  unknown  resistance. 
K,  K'  are  the  keys  for  closing  the  battery  and  galvanometer 
circuits,  respectively.  The  number  against  each  coil  rep- 
resents the  resistance  of  that  coil.  It  will  be  seen  that  with 
the  resistances  m.  A  B  C  D,  ,a  great  number  of  combinations 
can  be  made  with  suitable  cutting  in  or  cutting  out  of  coils 
by  means  of  the  plugs,  as  at  a,  b,  c,  d,  etc. 

Example. — 1.     If  in  the  figure,  as  shown,  the  galvanometer  shows 
no  deflection  on  pressing  the  keys  K,  K',  what  is  the  resistance  of  x  ? 

Solution. — In  arm  M {H  G)  the  10-ohm  coil  is  in  circuit,  the  others 
are   short-circuited   by   the  plugs  r,  s,  and  t(.     In  arm  N  {E  F)  the 
1,000-ohm  coil  is  in  circuit,  the  rest  being  short-circuited  by  the  plugs 
jt,  0,  and/.     In  arm  P  {A  B  C  D)  the  1,000,  100,  50,  one  20,  10,  one  2, 
and  one  1  ohm  coils  are  in  circuit,  the  rest  being  short-circuited  by  the 
plugs  b,  c,  d,  h,  J,  and  /.     The  resistances  are,  therefore, 
7^/=  10  ohms; 
7\^=  1,000  ohms; 
/'=  1,000  +  100  +  50  +  20  +  10  +  2  4-  1  =  1,183  ohms; 

and  by  formula  459,  X=-j^x  P,  or  t-tttttjX  1,183  =  11.83  ohms.  Ans. 


ELECTRICAL  MEASUREMENTS.  1641 

Example. — 2.  What  plugs  would  have  to  be  inserted  xvl  P  to  meas- 
ure a  resistance  of  21.7  ohms  in  x,  if  the  1-ohm  coil  only  be  used  in  M 
and  the  10-ohm  coil  only  be  used  in  A^? 

Ans.     a,  b,  c,  e,f,  g,  h,  I,  m,  or  a,  b,  d,  e,f,  g,  //,  k,  in. 

2512.  The  resistance  of  the  coils  is  usually  stamped  on 
the  top  of  the  box,  that  for  each  individual  coil  being 
marked  beside  the  space  between  the  brass  blocks  to  which 
the  coil  is  attached,  so  that,  after  having  made  the  necessary 
adjustments,  it  is  easy  to  read  off  the  resistance  in  either 
arm  of  the  bridge  by  adding  the  figures  opposite  the  spaces 
unfilled  by  plugs. 

The  coils  themselves  are  wound  on  spools  of  insulating 
material,  and  in  reliable  instruments  are  carefully  stand- 
ardized. In  order  that  the  current  flowing  through  a  re- 
sistance coil  of  a  considerable  number  of  turns  should  not 
create  a  magnetic  field  which  might  affect  the  galvanometer, 
the  coils  are  wound  non-indiictively;  that  is,  for  each  turn 
around  the  spool  in  one  direction  is  wound  a  turn  in  the 
opposite  direction,  so  that  the  magnetic  effects  are  neutral- 
ized. In  working  with  a  sensitive  galvanometer  this  precau- 
tion is  very  necessary.  The  usual  method  of  winding  the 
spool  is  to  measure  off  the  length  of  wire  required  and  fold 
it  in  the  middle;  then,  starting  at  this  fold,  the  two  parts  of 
the  wire  are  wound  on  as  one  wire.  A  current  circulating 
in  a  spool  so  wound  will  pass  through  one  half  the  wire  in 
one  direction  and  the  other  half  in  the  reverse;  so  the  mag- 
netic effects,  as  well  as  the  self-induction,  are  rendered 
practically  zero. 

In  making  resistance  measurements  with  a  Wheatstone 
bridge,  it  is  not  necessary  to  know  either  the  current  flowing 
or  the  E.  M.  F.  of  the  source  of  current;  so  almost  any 
source  of  a  steady  current  of  low  E.  M.  F.  is  suitable  for 
bridge  work.  It  is  customary  to  use  two  or  three  cells  of 
battery,  except  for  measuring  high  resistances,  when  more 
cells,  up  to  30  or  40,  should  be  used. 

2513.  For  measuring  low  resistances,  a  modification 
of  the  Wheatstone  bridge,  known  as  the  slide  -wire  or 
meter  bridge,  is  used.     A  diagram  of  this  bridge  is  shown 


1642 


ELECTRICAL  MEASUREMENTS. 


in  Fig.  1005.  A  wire  a  b  of  uniform  cross-section  is  stretched 
between  the  heavy  copper  blocks  c  and  d.  7?  is  a  known  and 
X  an  unknown  resistance,  both  of  which  are  connected  at 
one  end  to  the  heavy  copper  block  e,  and  at  the  other  to  the 
blocks  r  andd,  respectively.  The  galvanometer  is  connected 
between  the  block  e  and  a  contact  piece  n,  sliding  on  the  wire 
a  b.     It  will  be  seen  that  this  is  a  form  of  the  Wheatstone 


Fig.  1005. 
bridge  where  the  arms  M  and  N  are  replaced  by  R  and  a  n, 
and  the  adjustable  resistance  by  n  b.      From  the  considera« 
tion  of  the  principles  of  the  Wheatstone  bridge, 
R  :  X  \\  a  n   :   n  b\ 


or. 


X^Rv.—. 
an 


The  copper  blocks  c^  e,  and  dsive  made  heavy,  so  that  they 
will  introduce  no  appreciable  resistance  into  either  arm  of 
the  bridge.  As  the  wire  ^  ^  is  of  uniform  cross-section,  its 
absolute  resistance  need  not  be  known;  as  the  resistance  of 
the  two  parts  a  n  and  n  b  will  be  directly  proportional  to 
their  lengths,  the  formula 

an 
will  hold  good  if  a  n  and  n  b  represent  length  instead  of 
resistance.  It  is  not  even  necessary  to  know  the  actual 
lengths  of  a  n  and  n  b\  their  ratio  is  sufficient.  It  is  cus- 
tomary, however,  to  make  the  length  of  the  wire  a  b  one 
meter  in  this  form  of  slide-wire  bridge;  whence  the  name 
meter  bridge.  The  slider  n  is  usually  arranged  so  that  one 
end  slides  along  a  scale  the  length  of  the  wire,  divided  into 
any  convenient  number  of  divisions;  in  the  case  ot  a  meter 
bridge,  into  millimeters;  so  that  the   lengths  a  n  and    n  b 


ELECTRICAL  MEASUREMENTS. 


1G43 


may  be  read  directly  from  the  scale.  The  known  resistance 
R  is  not  usually  made  adjustable;  instead  standard coi/s  are 
used,  the  usual  sizes  being  0.1,  1,  and  10  ohms,  the  particular 
coil  used  being  selected  according  to  the  resistance  X  This 
makes  the  construction  of  the  bridge  much  cheaper  than  the 
ordinary  form,  and  as  standard  resistance  coils  of  great 
accuracy  may  be  purchased  already  prepared,  the  bridge 
may  be  cheaply  and  easily  constructed. 

2514.  These  standard  resistance  coils  are  usually  of 
the  form  shown  in  Fig.  lOOG.  The  resistance  coil  itself  is 
enclosed  in  a  brass  shell,  and 
the  whole  filled  with  paraffin. 
The  two  projecting  wires  are 
of  heavy  copper,  and  serve  as 
terminals.  In  order  to  insure 
good  contact,  when  great  ac- 
curacy of  measurement  is  re- 
quired, the  terminals  of  the 
copper  bars  c,  e,  and  d,  where 
the  resistances  R  and  X  are 
attached,  are  usually  made  in 
the  form  of  mercury  cups,  in- 
stead of  binding-posts,  so  that  D  Fig.  looe. 
in  connecting  the  standard  resistance  coil  it  is  only  neces- 
sary to  hang  the  ends  of  the  terminals  in  the  mercury  cups. 

It  is  not  at  all  necessary  that  the  wire  of  the  slide-wire 
bridge  be  stretched  out  straight,  as  shown  in  Fig.  1005. 
This  is  a  very  convenient  way  to  make  such  a  bridge,  but 
they  are  often  built  with  the  wire  wrapped  around  an  insu- 
lating cylinder,  or  stretched  around  the  edge  of  a  support, 
which  may  be  circular  or  square,  or  of  other  shape;  the 
main  point  being  to  support  a  length  of  wire  so  that  the 
ratio  of  the  distance  between  any  point  on  the  wire  and  one 
end  to  the  whole  length  of  the  wire  may  be  determined. 

2515.  The  slide-wire  bridge  is  more  especially  suited, 
as  stated,  to  the  measurement  of  low  resistances,  such  as 
determining  the  specific  resistance  of  metals,  etc.  The 
specific    resistance    of    a    conducting    substance    is    the 


1644 


ELECTRICAL  MEASUREMENTS. 


resistance  of  unit  length  of  unit  cross-section  of  that  sub- 
stance; that  is,  the  resistance  of  apiece  of  metal  1  centi- 
meter long,  whose  area  of  cross-section  is  1  square  centimeter, 
is  its  specific  resistance.  Expressed  in  ohms,  the  specific 
resistance  of  flint  glass  is  16,700,000,000,000,000,000,  and 
that  of  annealed  silver  is  .000001500,  their  ratio  being  about 
1  :  11,000,000,000,000,000,000,000,000.  To  prevent  the  con- 
stant repetition  of  zeros  in  writing  these  and  similar  values, 
prefixes  have  been  adopted  to  express  multiples  or  submul- 
tiples  of  a  unit,  as  per  the  following  list: 
MULTIPLES. 


Prefix. 

Amount  of  Multiplication. 

Expressed  in  "Words. 

Expressed  in  Figures. 

deka 

ten  times 

10 

10 

hecto 

one  hundred  times 

100 

10» 

kilo 

one  thousand  times 

1,000 

10^ 

mega 

one  million  times 

1,000,000 

10' 

bega 

one  billion  times 

1,000,000,000 

10^ 

trega 

one  trillion  times 

1,000,000,000,000 

10'» 

quega 

one  quadrillion  times 

1,000,000,000,000,000 

lO''' 

SUBMULTIPLES. 


Prefix. 

Amount  of  Division. 

Expressed  in  Words. 

Expressed  in  Figures. 

deci 

one-tenth 

lH-10 

10-' 

centi 

one-hundredth 

l-^100 

10-" 

milli 

one-thousandth 

1  ^  1,000 

10"= 

micro 

one-millionth 

1  ^  1,000,000 

10-" 

bicro 

one-billionth 

1  H-  1,000,000,000 

10-" 

tricro 

one-trillionth 

1  ^  1,000,000,000,000 

10-^' 

Using  these  prefixes,  the  specific  resistance  of  flint  glass 
would  be  said  to  be  16,700  quegohms  (16,700  X  1,000,000,- 
000,000,000  =  16,700,000,000,000,000,000  ohms)  and  that  of 
annealed  silver  1.500  microhms,  since 

1.500 


1,000,000 


.000001500  ohm. 


ELECTRICAL  MEASUREMENTS. 


1645 


In  Art.  2301    the  resistance  of  various  metals  for  1  inch 

of  length  and  1  square  inch  in  area  has  been  given.      These 

values  may  be  reduced  to  specific  resistance  by  performing 

the  necessary  calculations.     The  specific  resistances  of  some 

of  the  substances  commonly  termed  insulators  are  given  in 

Table  85. 

TABLE    85. 


Substance. 

Specific  Resistance. 

Mica 

84  tregohms 

Gutta-percha 

449  tregohms 

28  quegohms 

34  quegohms 

540  quegohms 

16,700  quegohms 

1  tregohm 

350  begohms 

Hard  rubber 

Paraffin 

Porcelain 

Flint  glass 

Olive  oil 

Lard  oil 

Table  86  gives  the  specific  resistance  of  some  of  the  more 
common  solutions  used  as  electrolytes. 

TABLE    86. 

Specific  resistance  of  various  electrolytes  in  ohms  at  50°  F 


Liquid. 


Copper  sulphate  \ 
Saturated  solution  ) 
Zinc  sulphate  ( 

Saturated  solution  [ 
Zinc  sulphate 
Common  salt 
Sal  ammoniac 
Sulphate  of  soda 
Sulphuric  acid 
Nitric  acid 
Hydrochloric  acid 


Specific 
Gravity. 


1.205 
1.440 


Solution 
giving 
least 
resist- 
ance. 


Specific 
Resistance. 


39.30 

33.60 

r28.22 
4.70 
2.50 

\  11.30 
1.38 
1.29 
1.32 


1646  .         ELECTRICAL  MEASUREMENTS. 

TEMPERATURE    COEFFICIENT. 

2516.  The  resistance  of  any  conducting  body  changes 
with  changes  in  the  temperature.  In  the  case  of  electro- 
lytes, non-metallic  substances  (insulators  and  carbon),  an 
increase  in  temperature  decreases  the  resistance,  while  in 
the  metals  and  their  alloys  an  increase  of  temperature 
increases  the  resistance.  The  percentage  of  change  of  re- 
sistance with  unit  change  of  temperature  is  known  as  the 
temperature  coefficient. 

Thus,  a  piece  of  copper  wire  which  is  known  to  have  a 
resistance  of  10  ohms  at  a  temperature  of  32°  F.  is  found 
to  have  a  resistance  of  11.11  ohms  at  82°  F.  These  changes 
in  resistance,  due  to  variations  of  temperature,  become 
quite  important  in  practical  work,  and  allowance  must  gen- 
erally be  made,  in  all  calculations  involving  conductors  sub- 
ject to  changes  of  temperature,  for  the  increase  or  decrease 
of  their  resistance. 

2517.  The  formulas  representing  the  effects  of  the 
increase  of  temperature  upon  the  conductivity  of  a  sub- 
stance may  be  written  as  follows: 

Assume  1\  =  original  resistance; 

r^  =  resistance  after  rise  of  temperature; 
a  =:  temperature  coefficient  for  each  degree  Cen- 
tigrade; 
h  =  temperature  coefificient  for  each  degree  Fah- 
renheit ; 
C°  =■  degrees    Centigrade    rise    of    temperature 

(See  Table  88.) 
F°  =  degrees  Fahrenheit  rise  of  temperature. 

Then,  r,  =  r,  [1 -\- a  C°),  (460.) 

and  r^  =  7\{l-{-dF°).  (461.) 

The  values  of  a  and  d  may  be  found  in  Table  87. 

2518.  The  formulas  for  the  decrease  of  resistance 
with  decrease  oi  temperature  may  likewise  be  stated. 

Let    Tj  =  original  resistance; 

r,  =  resistance  after  lowering  of  temperature; 


ELECTRICAL  MEASUREMENTS. 


1647 


a  =  temperature  coefficient  for  each  degree  Centi- 
grade; 
b  =  temperature    coefficient  for  each  degree   Fah- 
renheit ; 
C°  =  degrees  Centigrade  fall  of  temperature; 
F°  =  degrees  Fahrenheit  fall  of  temperature. 

Then,  r,=  ^    /V°-  (462.) 


r,  = 


r. 


(463.) 


l  +  /^i^°* 
TABLE    87. 

TEMPERATURE  COEFFICIEIVTS  FOR  VARIOUS  METALS. 


Name  of  Metal. 

For  Centigrade. 
(a) 

For  Fahrenheit. 

Silver 

.00377 
.00388 
.00365 
.00390 
.00247 
.00453 
.00365 
.00387 
.00389 
.00354 
.00088 
.00044 

.002094 

Copper 

Gold 

.002156 
,002028 

Aluminum 

.002167 

Platinum 

Iron 

.001372 
.002517 

Tin 

.002028 

Lead 

.002150 

Antimony ■ 

.002161 

Bismuth 

Mercury 

German  silver 

.001967 
.000489 
.000244 

Example. — A  copper  conductor  has  a  resistance  of  15  ohms  at  a 
temperature  of  20°  C.  What  will  be  its  resistance  (a)  at  50°  C.  ? 
(3)  at  8°  C.  ? 

Solution. — {a)  The  original  resistance  =  15  ohms  =  ri.  The 
change  in  temperature  is  50°  —  20°  =  30°  C.  =  C°.  Then,  since  this  is 
an  increase,  formula  460  will  apply,  for  which,  from  Table  87, 
a  =  .00388  for  copper,  and  we  have  ra  =  15  [1  +  (.00388  X  30)J  =  16.746 
ohms.     Ans. 

{d)  In  this  case  the  change  of  temperature  is  a  decrease,  and  C  = 
20  —  8  =  12.  Then,  by  formula  462,  the  changed  resistance  rj  = 
15 


1  + (.00388X12) 


=  14.33  ohms.     Ans. 


1648 


ELECTRICAL  MEASUREMENTS. 


For  metals  having  a  different  temperature  coefficient 
from  that  of  copper,  the  foregoing  formulas  should  be 
changed  by  inserting  the  proper  constant,  taken  from  Table 
87,  in  place  of  .00388  or  .00215G. 

2519a  The  following  table  of  Centigrade  and  Fahren- 
heit degrees  is  given  to  facilitate  the  rapid  conversion  from 

one  scale  to  another. 

TABLE    88. 

TABLE  OF  CENTIGRADE  AND   FAHRENHEIT  DEGREES. 


Deg. 
C. 

Deg. 
F. 

Deg. 
C. 

Deg. 
F. 

Deg. 
C. 

Deg. 
F. 

Deg. 
C. 

Deg. 

F. 

0 

32.0 

26 

78.8 

51 

123.8 

76 

168.8 

1 

33.8 

27 

80.6 

52 

125.6 

77 

170.6 

3 

35.6 

28 

82.4 

53 

127.4 

78 

172.4 

8 

37.4 

29 

84.2 

54 

129.2 

79 

174.2 

4 

39.2 

30 

86.0 

55 

131.0 

80 

176.0 

5 

41.0 

31 

87.8 

56 

132.8 

81 

177.8 

6 

42.8 

32 

89.6 

57 

134.6 

82 

179.6 

7 

44.6 

33 

91.4 

58 

136.4 

83 

181.4 

8 

46.4 

34 

93.2 

59 

138.2 

84 

183.2 

9 

48.2 

35 

95.0 

60 

140.0 

85 

185  0 

10 

50.0 

36 

96.8 

61 

141.8 

86 

186.8 

11 

51.8 

37 

98.6 

62 

143.6 

87 

188.6 

12 

53.6 

38  " 

100.4 

63 

145.4 

88 

190.4 

13 

55.4 

39 

102.2 

64 

147.2 

89 

192.2 

14 

57.2 

40 

104.0 

65 

149.0 

90 

194.0 

15 

59.0 

41 

105.8 

66 

150.8 

91 

195.8 

16 

60.8 

42 

107.6 

67 

152.6 

92 

197.6 

17 

63.6 

43 

109.4 

68 

154.4 

93 

199.4 

18 

64.4 

44 

111.2 

69 

156.2 

94 

201.2 

19 

66.2 

45 

113.0 

70 

158.0 

95 

203.0 

20 

68.0 

46 

114.8 

71 

159.8 

96 

204.8 

21 

69.8 

47 

116.6 

72 

161.6 

97 

206.6 

22 

71.6 

48 

118.4 

73 

163.4 

98 

208  4 

23 

73.4 

49 

120.2 

74 

165.2 

99 

210.2 

24 

75.2 

50 

122.0 

75 

167.0 

100 

212.0 

25 

77.0 

ELECTRICAL  MEASUREMENTS.  1649 

Relations  of  Thertnometric  Scales  ; 

L — To  convert  Fahrenheit  to  Centigrade^  subtract  32,  mul- 
tiply by  5,  and  divide  by  9. 

For  example,  50°  Fahrenheit  =  (^Q~^^)^  =  10°  Centi- 
grade. 

IL — To  convert  Centigrade  to  Fahrenheit ^  multiply  by  9, 

divide  by  J,  and  add  82. 

Q  V  TOO 
For  example,  100°  Centigrade  =     ^/      +  32  =  212°  Fah- 

0 

renheit. 

INSULATION. 

2520.  In  order  to  transmit  electricity  from  one  point 
to  another,  that  is,  to  make  the  electric  current  follow  a 
definite  path  in  a  conductor,  it  is  necessary  that  the  con- 
ductor should  be  separated  from  all  points  between  which 
and  the  conductor  there  is  a  difference  of  potential  by  sub- 
stances whose  resistance  is  so  high  that  that  difference  of 
potential  can  establish  no  appreciable  current. 

If  two  conductors  supplying  current  to  a  lamp,  for  exam- 
ple, were  laid  directly  on  the  ground,  the  current  would 
flow  directly  from  one  conductor  to  the  other  through  the 
earth,  the  earth  being  a  good  conductor.  If  the  wires  be 
surrounded  by  glass  tubes,  the  resistance  offered  to  the  pas- 
sage of  the  current  from  wire  to  wire  through  the  glass  and 
the  earth  would  be  so  great  that  the  current  would  be 
infinitesimal,  and  the  full  strength  of  the  current  could  be 
utilized  in  the  lamp.  Or,  if  the  wires  were  suspended  in 
the  air  upon  glass  knobs  attached  to  poles,  again  the  resist- 
ance between  conductors,  or  from  the  conductors  to  the 
earth,  would  be  comparatively  enormous.  This  resistance  is 
known  as  the  insulation  resistance  of  the  circuit,  and,  it 
is  obvious,  should  be  as  great  as  possible. 

;S521.  In  almost  all  electrical  appliances,  insulating 
materials  are  as  necessary  as  conducting  materials,  and  the 
measurement  of  the  insulation  resistance  of  such  apparatus 
is  often  very  important. 


1650 


ELECTRICAL  MEASUREMENTS. 


In  telegraph  and  telephone  line  construction,  bare  iron  or 
copper  wires  are  used,  and  are  supported  on  glass  knobs. 
From  the  high  specific  resistance  of  glass,  it  would  be  rea- 
sonable to  suppose  that  this  would  insulate  the  wires  very 
thoroughly  from  the  earth,  which  would  be  the  case  were  it 
not  for  the  fact  that  the  surface  of  the  glass  insulators  is 
always  covered  with  a  film  of  dust  and  moisture,  which  is  of 

much    less    resistance    than     the 
glass.      Glass  insulators  are,  there- 
.  fore,  made  so  as  to  give  a  consid- 

erable length  of  surface  between 
the  point  of  attaching  the  wire 
and  the  point  of    support  of  the 

(C  glass.      Fig.    1007    shows  such  an 

^^^^- ^  "sSiSr  &  & 

^^^iic;::::;.:.:.^^^'\  insulator,  which  is  supported  by  a 

/^^^^H^          ^^^  \         wooden  pin  with  a  thread  cut  on 
M^^^^^-" §^^^  fe-    t^''^    end,   which    screws    into   the 

thread    moulded    in   the    glass  B. 

The  wire  being   fastened    in    the 
Fig.  loor.  groove  C,  any  leakage  of  current 

from  the  wire  must  pass  over  the  surface  of  the  glass  from 
C  to  the  supporting  pin.  The  length  of  this  surface  is  ma- 
terially increased  by  the  groove  A.  This  form  of  insulator 
is  known  as  a  petticoat  insulator. 

The  insulation  resistance  of  one  of  these  insulators  would, 
of  course,  be  very  high,  even  if  considerable  moisture  were 
present,  but  as  in  a  long  line  strung  on  these  insulators  the 
insulation  resistances  are  all  in  multiple,  the  total  insulation 
resistance  of  the  line  may  be  low. 

2522.  Fig.  1008  shows  an  easy  method  of  testing  the 
approximate  resistance  of  a  line  L,  in  which  6^  is  a  galva- 
.nometer,  B  a  battery,  and  R  a  known,  resistance,  which 
should  be  high,  say  10,000  ohms.  iT  is  a  key  or  switch, 
which,  when  contact  is  made  with  terminal  b,  connects  the 
resistance  R  through  the  galvanometer  to  the  battery  B\ 
when  contact  is  made  to  the  terminal  a,  the  battery  is  con- 
nected to  the  earth  by  the  earth  plate  E,  which  may  be  a 


ELECTRICAL  MEASUREMENTS. 


1651 


metal  plate  buried  in  moist  earth,  or  the  wire  may  be  at- 
tached to  a  water  or  gas  pipe,  which,  being  buried  in  the 
earth,  makes  an  excellent  earth  connection. 

By  connecting  the  battery  to  the  resistance  R  by  means  of 
the  switch  K,  the  needle  of  the  galvanometer  will  be  de- 


FlG.  1008. 

fleeted  a  certain  amount,  which  should  be  noted.  Then,  on 
connecting  the  battery  to  the  earth  plate  E,  the  circuit  will 
be  completed  through  the  insulation  resistance  between  the 
line  L  and  the  earth.  The  current  flowing  will  again  pro- 
duce a  deflection  of  the  galvanometer  needle.  The  currents 
which  flow  through  the  known  resistance  R  and  the  insula- 
tion resistance  of  the  line  L  will  be  inversely  proportional  to 
those  resistances;  so,  knowing  the  galvanometer  constant, 
the  currents  and,  from  their  ratio,  the  insulation  resistances 
of  the  line  may  be  calculated. 

If  a  tangent  galvanometer  be  used,  the  resistances  will  be 
inversely  proportional  to  the  tangents  of  the  angles  of  deflec- 
tion ;  that  is, 

R  :   tan  d^  =  I  '.  tan  d, 

where  R  =  known  resistance; 

/  =  insulation  resistance; 

dz=  the  angle  of  deflection  when  R  is  in  circuit; 
</,  =  the  angle  of  deflection  when  /  is  in  circuit. 

From  the  above  proportion, 


/  = 


R  tan  d 
tan  d. 


(464.) 


That  is,  the  insulation  resistance  of  a  line  is  equal  to  a 


1653  ELECTRICAL  MEASUREMENTS. 

given  resistance  multiplied  by  the  quotient  obtained  by  divi- 
ding the  tangent  of  the  angle  of  galvanometer  deflection  when 
that  resistance  is  in  circuit  by  the  tangent  of  the  angle  of  de- 
flection when  the  circuit  is  through  the  line. 

Example. — The  known  resistance  =  10,000  ohms  ;  the  deflection  of 
the  galvanometer  when  R  was  in  circuit  was  60°  ;  the  deflection  of  the 
galvanometer  when  /  was  in  circuit  was  33°  \  what  was  the  insulation 
resistance  of  the  line  in  ohms  ? 

Solution. — tan  d°  =  1.733. 
tan  d°i  —    .649. 

J?  =  10,000  ;  therefore,  by  formula  464, 

-.      10,000x1.732      _^_„    ,  ,  . 

/=  — ;QTr =  26,700  ohms,  nearly.     Ans. 

.b49 

2>52'3»  As  the  number  of  paths  for  the  current  through 
the  insulation  increases  with  the  length  of  the  line,  the  in- 
sulation resistance  of  the  line  decreases  as  the  length  of  the 
line  increases ;  so  the  total  insulation  resistance  multiplied 
by  the  length  of  the  line  gives  the  insulation  resistance  per 
unit  of  length.  The  usual  unit  of  length  for  overhead  tele- 
graph and  telephone  lines  is  one  mile. 

Example. — What  is  the  insulation  resistance  per  male  in  the  above 
example  if  the  line  be  7.5  miles  long  ? 

Solution.—  26,700  X  T.5  =  200,250  ohms,  or  .2  megohm,  practically. 

Ans. 

This  is  about  the  insulation  resistance  required  for  ordi- 
nary telegraph  and  telephone  work. 

The  above  method  of  testing  requires  a  sensitive  galva- 
nometer of  fairly  low  resistance,  and  gives  approximately 
precise  results  for  resistances  not  exceeding  about  30,000 
ohms. 

If  the  resistance  much  exceeds  this  limit,  a  shunt  may  be 
used  with  the  galvanometer  of  any  convenient  multiplying 
power;  for  example,  100.  The  deflection  through  the  known 
resistance  being  noted,  the  shunt  should  be  removed  for 
the  line  resistance  measurement.     Thus,  a  current  through 

the  insulation  resistance  of  — -—  of  the  current  through  the 

71  -\-\ 

known  resistance  (in  the  above  case  -j^xr)  '^'^  give  the  same 


ELECTRICAL  MEASUREMENTS. 


1653 


deflection,  and  the  line  insulation  resistance  will  be  a  corre- 
sponding multiple  of  the  known  resistance. 

To  obtain  more  accurate  results,  allowance  must  be  made 
in  each  case  for  the  resistance  of  the  galvanometer  and  bat- 
tery. Usually,  these  are  not  a  sufificient  per  cent,  of  the 
total  resistance  of  either  circuit  to  affect  the  result  much. 

252/4:0  Another  good  method  of  measuring  insulation 
resistance  is  to  make  this  resistance  one  arm  of  a  Wheat- 
stone  bridge,  as  represented  in  Fig.  1009.     By  making  the 


#~ 


Fig.  1009, 

resistance  of  AI  great  in  proportion  to  N,  resistances  as  high 
as  2,000,000  ohms  may  be  measured  with  a  bridge  as  ordi- 
narily arranged.      (See  Fig.  1004.)  * 

2525.  By  grounding  the  distant  end  of  the  line  L, 
the  resistance  of  the  conductor  which  makes  up  the  line 
may  be  measured  by  the  same  methods.  Grounding  a  cir- 
cuit consists  in  connecting  it  electrically  with  the  earth, 
usually  by  means  of  a  metal  plate  buried  in  moist  earth,  or  to 
the  pipes  of  a  water  or  gas  system.  Grounding  is  conven- 
tionally represented  as  at  E^  Figs.  1008  and  1009.  The  re- 
sistance of  the  earth  is  so  slight  that  for  small  currents  it 
may  be  usually  neglected,  if  the  grounding  is  well  done. 

2526.  The  insulation  resistance  of  apparatus  for  elec- 
tric light  and  power  work  must  be  considerably  greater  than 
that  for  telegraph  and  telephone  use,  and  the  wire  used  is, 
except  in  special  cases,  covered  with  insulation  instead  of 
being  bare. 


1654  ELECTRICAL  MEASUREMENTS. 

This  insulation  must  not  only  have  a  high  specific  resist 
ance,  but  it  must  be  able  to  meet  various  other  require- 
ments. In  wire  for  overhead  construction,  for  example,  the 
insulation  must  stand  the  abrasion  of  tree  branches,  etc.,  be 
reasonably  fireproof,  water-proof,  able  to  withstand  the 
action  of  the  weather,  and  flexible  enough  to  allow  the  wire  to 
be  reeled  or  strung  in  place  without  injury  to  the  insulation. 
It  is  obvious  that  many  substances  of  high  specific  resist- 
ance, such  as  glass  or  porcelain,  would  not  fill  some  of  the 
above  conditions.  In  fact,  there  is  scarcely  any  one  sub- 
stance that  would  answer.  The  best  grades  of  insulated 
wire  are  usually  made  with  a  layer  of  rubber,  or  some  com- 
pound composed  largely  of  rubber,  surrotmding  the  wire, 
and  protected  by  an  additional  covering  of  braided  cotton  or 
similar  device,  soaked  in  some  reasonably  fireproof  and 
weather-proof  compound. 

In  order  to  thoroughly  test  the  insulation  resistance,  con- 
tact should  be  made  with  the  whole  outer  surface  of  the 

insulation.  This  is  best 
done  by  immersing  the 
wire  in  a  tank  of  water, 
slightly  salted  to  make  it 
conducting,  as  shown  in 
Fig.  1010.  The  tank  is  of 
metal,  and  the  insulation  resistance  is  measured  between 
the  water  surrounding  the  wire  and  the  wire  itself,  as  shown 
at  a  b.  Connection  with  the  water  is  made  by  a  binding- 
post  attached  to  the  metal  tank,  or  if  the  tank  be  glass  or 
china,  a  metal  plate  is  used,  dipping  in  the  water. 

2527.  A  long  piece  of  wire  prepared  for  test  in  this 
way  would  have  a  large  area  of  insulating  material  between 
two  conducting  bodies,  i.  e.,  the  wire  and  the  water.  On 
connecting  the  wire  and  water  to  the  poles  of  a  battery,  a 
charge  of  electricity  will  spread  itself  over  the  inner  and 
outer  surfaces  of  the  insulation,  which  will  cause  a  momen- 
tary rush  of  current  from  the  battery.  Another  phenomenon 
which  also  appears  is  that  known  to  telegraph  engineers  as 


Fig.  1010. 


ELECTRICAL  MEASUREMENTS.  1655 

electrification.  The  exact  nature  of  this  phenomenon  is 
not  known,  but  it  has  been  held  by  eminent  authority  to  be 
2i polarization  of  the  insulation,  and  its  effect  is  to  cause  a  con- 
tinuation of  the  first  rush  of  current  due  to  the  static 
charge,  that  gradually  grows  smaller  and  smaller,  until 
after  the  lapse  of  some  few  minutes  the  current  becomes 
steady.  On  disconnecting  the  battery  and  replacing  it  with 
a  piece  of  wire,  a  back  current  will  flow  through  the  wire 
from  surface  to  surface  of  the  insulation  until  it  is  depolar- 
ized. 

In  testing  the  insulation  resistance  of  long  pieces  of  wire 
in  water,  these  effects  may  interfere  materially  with  read- 
ings, especially  if  the  Wheatstone  bridge  method  be  used. 
With  the  following  methods  of  testing,  however,  it  is  usually 
sufficient  to  wait,  after  closing  the  current,  until  the  current 
has  become  steady  before  taking  readings. 

In  testing  long  cables  for  submarine  use,  or  long  pieces 
of  wire,  it  is  sometimes  customary  to  take  the  resistance 
readings  after  the  electrification  has  continued  for  a  certain 
definite  time,  usually  1  minute.  This  is  always  so  stated  in 
the  results  of  the  test,  thus:  "  Insulation  resistance  per  mile 
after  1  minute's  electrification,  400  megohms. " 

Where  the  surface  area  of  the  insulation  is  small,  the  elec- 
trification is  hardly  perceptible,  and  ordinarily  will  have  no 
effect  on  the  readings,  even  if  a  bridge  be  used. 

2528.  The  following  method  is  like  that  described  in 
Art.  2522,  Fig.  1008,  except  that  as  the  insulation  resist- 
ance of  a  short  length  of  well-insulated  wire  would  be  quite 
high,  it  would  probably  be  necessary  to  use  a  shunt  with  the 
galvanometer. 

Fig.  1011  is  a  diagram  of  connections  for  such  a  measure- 
ment. The  shunt  S  is  connected  in  parallel  with  the  gal- 
vanometer G  by  inserting  a  metal  plug  between  the  metal 
blocks  at  a.  The  switch  K  connects  either  the  metal  tank 
T  or  the  known  resistance  R  with  the  battery  B. 

The  best  method  of  procedure  is  to  first  read  the  deflec- 
tion through  the  insulation  resistance  of  the  wire  P^witb 


1656 


ELECTRICAL  MEASUREMENTS. 


the  shunt  disconnected.      Then    connect  in  the  fhunt  and 
read  the  deflection  through  the  known  resistance  R,  chan- 
ging the  shunt  vS"  until  the  deflection  is  approximately  the 
G  V 


Fig.  1011. 

same  as  before.  Then,  knowing  the  multiplying  power  of 
the  shunt  used,  the  insulation  resistance  of  the  wire  may  be 
calculated  as  in  Art.  2522. 

Example. — In  a  tangent  galvanometer  the  resistance  is  600  ohms; 
deflection  through  insulation  =  38° ;  with  a  shunt  of  8  ohms,  deflection 
through  resistance  =  42° ;  resistance  i?  =  10,000  ohms.  What  is  the 
insulation  resistance  ? 

Solution. — Multiplying  power  of  shunt  =  ^^  +  1  =  76. 

The  deflection  through  the  resistance  =  (/°  =42,  and  the  deflection 
through  the  insulation  =  ^°i=  38.     Then,  tan  ^"  =  .9004;  tan  </°i=. 7813. 

To  get  the  true  value  of  the  current  in  resistance  i?,  tan  (^°  must  be 
multiplied  by  the  multiplying  power  of  the  shunt. 

.9004  X  76  =  68.43  =  tangent  of  the  angle  to  which  needle  would  be 
deflected  if  shunt  were  not  used.  (68.43  is  the  tangent  of  about  89°  10', 
at  which  point  a  tangent  galvanometer  could  not  possibly  be  read  with 
a  precision  of  under  50^.) 

By  formula  464, 


/= 


10,000  X  68.43      684,300 


7813 


.7813 


=  876,000  ohms,  nearly.     Ans. 


2529.  It  is  evident  that  the  theory  of  the  above  method 
of  testing  insulation  resistance  is  that,  if  the  voltage  of  the 
battery  be  constant,  the  current  sent  through  the  two  resist- 
ances will  be  inversely  proportional  to  those  resistances. 

The  current  from  the  battery  is  very  small  in  either  case, 
although  when  passing  through  the  resistance  R  it  is  about 


ELECTRICAL  MEASUREMENTS. 


1657 


70  times  as  much  as  when  the  insulation  resistance  is  in  cir- 
cuit. This  difference  would  scarcely  affect  an  ordinary- 
battery,  and  as  the  actual  insulation  resistance  of  a  speci- 
men of  wire  is  seldom  wanted  with  an  accuracy  greater  than 
95-90^  (that  is,  within  5  or  lOfo),  this  method  gives  good 
results. 

2530.  Another  method  of  measuring  insulation  resist- 
ance that  does  not  require  the  use  of  a  shunt  with  the  galva- 
nometer is  shown  in  Fig.  1012.     To  make  the  test,  a  battery 


ICell 


(ai 


(b) 

Fig.  1012. 


ii|i|i|-    100 Cells  |i|i|i|f1 


of  100  cells  is  required.  The  cells  should  be  uniform  in  kind, 
size,  and  condition. 

The  galvanometer  should  be  connected  in  series  with  the 
insulation  resistance  and  the  cells,  as  shown  in  Fig.  1012  (d), 
and  the  deflection  noted. 

The  galvanometer  should  then  be  connected  in  series  with 
one  cell  of  the  battery  and  a  known  adjustable  resistance, 
which  should  be  high  (say  10,000  ohms,  as  before),  and  the 
deflection  under  these  conditions  [Fig,  1012  (a)]  noted. 
The  resistance  should  be  adjusted  so  as  to  give  about  the 
same  deflection  as  the  first  reading. 

It  is  evident  that  the  100-cell  battery  would  give  100  times 
the  current  through  the  resistance  and  galvanometer  that 
the  single  cell  does,  and  assuming  that  the  angle  of  de- 
flection of  the  galvanometer  is  directly  proportional  to  the 
current  flowing,  100  times  the  deflection,  if  that  were  pos- 
sible. So,  calling  d  the  deflection  through  the  resistance, 
with  1  cell,  then  100  d  would  be  the  deflection  with  100 
cells;  but  the  deflection  through  the  insulation  resistance 
with  100  cells  is  known;  call  it  d^. 


1658  ELECTRICAL  MEASUREMENTS. 

Then,  as  before,  /  :  R::  100 d  :  ^„  or  if  ^  =  the  number  of 
cells  and  R  =  the  extra  resistance, 

1=^^.  (465.) 

That  is,  the  insulation  resistance  of  a  cable  is  equal  to  a 
given  resistance  multiplied  by  the  quotient  obtained  by  divi- 
ding the  deflection  through  the  given  resistance  with  one  cell  by 
the  deflection  through  the  cable  with  a  number  of  cells,  this 
product  being  multiplied  by  that  number. 

Example. — If  the  deflection  with  100  cells  through  the  insulation 
resistance  was  37,  and  through  9,000  ohms  with  1  cell  was  43,  what  was 
the  insulation  resistance  ? 

Solution. — In  this  example  the  given  resistance  =  9,000  ohms  =  R  ; 
the  deflection  through  this  resistance  with  1  cell  =  42°  =  d  ;  the  number 
of  cells  used  for  the  insulation  test  =  100  =  x\  and  the  deflection  through 
the  insulation  with  these  cells  =  37°  =  rt'i.     Then,  by  formula  465, 

-.      9,000  X 100  X  43      .......    ,  ,  ,  .  ,  . 

/= — =  1,020,000  ohms,  nearly,  or  about  1  megohm.   Ans. 

o  i 

This  method  is  based  upon  the  supposition  that  the  avail- 
able E.  M.  F.  of  the  battery  will  be  directly  proportional  to 
the  number  of  cells,  which,  with  a  little  care  in  the  selection 
of  cells,  will  be  the  case,  and  that  the  current  taken  from 
the  cells  will  not  be  great  enough  with  either  measurement 
to  affect  the  E.  M.  F.,  which  will  again  be  the  case,  and  the 
precision  of  this  form  of  test  will  be  amply  good  for  most 
insulation  measurements. 

2531.  As  many  insulations  deteriorate  after  having 
been  under  water  some  time,  readings  should  be  taken  of  the 
insulation  resistance  at  intervals  during  a  considerable  time 
to  observe  this  deterioration,  if  there  be  any.  For  example, 
readings  taken  after  the  wire  had  been  immersed  15  minutes, 
1  hour,  3  hours,  10  hours,  24  hours,  would  show  any  effect 
that  wetting  would  have  that  would  be  serious. 

If  a  break  occur  in  the  insulation  under  the  water,  the  water 
will  come  in  contact  with  the  metal  wire,  and  the  ensuing 
electrolysis  will  liberate  bubbles  of  gas,  which  will  alternately 
collect  and  pass  off  at  the  break.     This  will  so  vary  the  resist- 


ELECTRICAL  MEASUREMENTS.  1659 

ance  that  the  current  will  not  be  steady  enough  to  allow  its 
value  to  be  read.  The  galvanometer  needle  will  irregularly 
swing  back  and  forth,  and  it  will  be  useless  to  attempt  to 
measure  the  insulation  resistance,  especially  as  the  action 
would  indicate  defective  insulation. 

2532.  It  is  not  altogether  necessary  to  immerse  the 
wire  in  water,  although  this  is  very  convenient,  as  the  water 
makes  contact  with  the  entire  outer  surface  of  the  insulation, 
as  the  wire  does  with  the  entire  inner  surface,  besides  test- 
ing the  water-proof  qualities^  the  insulation. 

For  some  tests  the  wire  may  be  closely  wrapped  around  a 
smooth  bright  metal  bar — a  section  of  shafting  for  example — ■ 
and  the  resistance  between  this  bar  and  the  wire  measured. 
Or  two  pieces  of  the  wire  maybe  twisted  together,  and  the 
resistance  between  the  two  wires  measured. 

It  is  often  desirable  to  test  the  insulating  qualities  of 
sheets  of  paper,  mica  fiber,  or  similar  substances.  A  con- 
venient way  to  prepare  them  for  such  a  test  is  to  make  two 
smooth  brass  plates  smaller  than  the  pieces  of  insulation  to 
be  tested,  which  should  be  placed  between  them.  The 
insulation  resistance  may  then  be  measured  between  the  two 
brass  plates,  and  from  the  area  and  length  (thickness)  of  the 
piece  of  insulation  between  the  plates  its  specific  resistance 
may  be  calculated.  Another  way  is  to  wrap  the  insulation 
around  a  smooth  metal  bar  as  before — apiece  of  shafting  for 
example — and  bind  the  outside  closely  with  fine  bare  copper 
wire.  The  insulation  resistance  may  then  be  measured 
between  the  wire  and  the  bar.  Many  other  methods  of  pre- 
paring insulation  for  tests  will  suggest  themselves  as  occasion 
requires. 

ELECTRICAL     APPARATUS. 

2533.  The  following  is  a  description  of  the  free  electrical 
apparatus  with  which  the  student  is  furnished  in  connection  with  this 
subject.  Directions  are  given  for  performing  certain  experiments  cal- 
culated to  help  the  student  to  a  better  understanding  of  the  subject  of 
Electrical  Measurements.  Unless  the  student  has  had  previous  instruc- 
tion of  a  like  nature,  he  is  earnestly  requested  (though  not  required)  to 


1660 


ELECTRICAL  MEASUREMENTS. 


make  all  the  experiments  mentioned,  and  to  keep  a 
record  of  his  results  by  answering  the  questions  under 
the  heading  Experiments  with  Electrical  Apparatus, 
which  follows  the  description  of  the  instruments.  He 
may  forward  his  record  to  the  School,  if  he  so  desires, 
for  correction  and  approval  when  he  sends  his  answers 
to  the  questions  on  Electrical  Measurements,  but  he 
will  be  marked  and  his  work  computed  in  connection 
with  his  work  on  the  questions  above  referred  to. 


DESCRIPTION     OF    APPARATUS. 

2534,     The   Slide-Wire  Bridge.— This 

is  a  Wheatstone  bridge  of  the  shde-wire  form 
(Art.  2513),  and  is  illustrated  in  Fig.  1013. 
The  slide  wire  W,  made  of  German  silver  wire, 
is  stretched  across  a  scale  S,  of  the  same  length 
as  the  wire,  divided  into  1,000  equal  divisions, 
every  5th  division  being  marked,  and  every 
2  50th  division  numbered,  in  both  directions, 
o  starting  from  each  end.  Three  strips  of  cop- 
per C,  C,  C"  are  fastened  to  the  board,  as 
shown,  and  to  these  are  screwed  the  terminals 
a  and  b;  c,  d,  and  c;  /"and  g,  respectively. 

From  an  inspection  of  the  figure,  it  will  be 
seen  that  the  strip  C  corresponds  to  the  piece 
d  in  Fig.  1005;  C  corresponds  to  the  middle 
section  e,  and  C"  to  the  piece  c  in  the  same 
figure. 

The  resistance  coils  furnished  for  use  with 
this  bridge  are  of  the  form  illustrated  in  Fig. 
1014.  The  resistance  coil  is  made  up  of  a  coil 
of  German  silver  wire  R,  insulated  with  silk, 
wound  on  a  wooden  bobbin,  or  spool,  5. 
Through  the  head  of  the  spool  two  pieces  of 
heavy  copper  wire  /,  t  are  driven,  the  ends  of 
the  resistance  coil  being  soldered  to  these 
wires;  they  form  the  terminals  of  the  coil. 
The   two  wires  (/,  t)  are   the   same   distance 


ELECTRICAL  MEASUREMENTS. 


1661 


apart  as  the  holes  in  the  terminals  b,  c  or  e,  f,  Fig.  1013,  so 
that  a  coil  may  readily  be  connected  in  its  proper  position  by 


Fig.  1014. 

slipping  the  two  terminal  wires  through  those  holes,  and 
clamping  them  in  position  by  means  of  the  milled-head 
screws. 

With  each  bridge  are  furnished  two  resistance  coils,  one 
of  1  ohm,  the  other  of  about  10.5  ohms,  resistance.  These 
may  be  readily  distinguished,  as  the  1-ohm  coil  is  covered 
with  a  strip  of  leather,  while  the  wire  of  the  other  is  ex- 
posed. Also,  the  10.5-ohm  coil  is  made  of  much  finer  wire 
than  that  used  for  the  1-ohm  coil. 


2535.  The  galvanometer  is  a  combination  tangent 
and  detector  galvanometer,  available  for  use  in  either 
capacity.  The  detector  gal- 
vanometer consists  of  a  coil  of 
insulated  wire  wound  on  a 
wooden  form,  and  divided  in 
the  center  to  allow  for  the  sup- 
port of  a  magnetic  needle 
which  swings  in  the  center  of 
the  coil.  A  perspective  section 
of  the  coil  and  its  support  is 
shown  in  Fig.  1015.  Here  B  represents  the  wooden  form  on 
which  the  coil  is  wound  in  two  parts,  C  C  and  C  C .      An 


Fig.  1015. 


1663  ELECTRICAL  MEASUREMENTS. 

opening  is  made  in  the  form,  passing  completely  through 
the  coils,  thus  forming  the  space  S  in  which  the  magnetic 
needle  is  free  to  swing.  Another  opening  O  is  made  in 
the  top  of  the  partition  between  the  two  parts  of  the  coil, 
extending  through  to  the  space  S.  This  provides  a  means 
for  placing  the  magnetic  needle  in  position.  In  the  center 
of  the  wooden  form  is  placed  an  ordinary  steel  needle  N._ 
extending  nearly  to  the  top  of  the  coils  in  the  center  of  the 
opening  O ;  this  needle  forms  the  pivot  on  which  the  mag- 
netic needle  swings. 

The  magnetic  needle  and  the  pointer  that  is  attached  to 
it  are  illustrated  in  Fig.  1016.  The  construction  is  as  fol- 
lows: The  magnetic  needle  M  is  made  from  a  piece  of  fiat 
steel  about  ^  inch  long  and  -^-^  inch  wide,  pointed  at  the 
ends.     Before  being  hardened,  a  hole  is  punched  in  the  cen- 


FlG.  1016. 


ter  of  this  piece,  and  when  the  piece  has  been  hardened 
and  magnetized,  a  short  glass  tube  G,  closed  at  the  top,  is 
fastened  in  the  hole.  This  forms  the  bearing  which  rests 
on  the  pivot  in  the  center  of  the  coils;  the  smooth  glass 
surface  resting  on  the  steel  point  makes  a  bearing  that  is 
remarkably  free  from  friction,  so  that  the  galvanometer  is 
very  sensitive.  The  pointer  which  indicates  the  deflection 
of  the  needle  is  a  fine  glass  rod  P,  blackened  at  the  ends, 
and  attached  in  the  middle  to  a  light  tin  tube  T,  which 
slides  over  the  glass  bearing  G,  and  is  held  in  place  by  its 
friction  with  the  bearing. 

The  coils  and  pivot  are  mounted  in  the  center  of  a  cir- 
cular wooden  case  that  is  turned  from  a  solid  block;  a  paper 
scale  is  mounted  over  the  coils,  and  is  divided  on  one  side 
into  degrees  (numbered  to  90  by  tens  each  way  from  a  zero 


ELECTRICAL  MEASUREMENTS. 


1663 


mark),  and  on  the  other  side  the  scale  is  marked  to  repre- 
sent tangents.  The  ends  of  the  pointer  on  the  needle  move 
over  the  scale  divisions  and  indicate  the  angle  of  deflection 
of  the  needle.  The  whole  is  protected  by  a  circular  glass 
cover,  held  in  place  by  a  ring  of  brass  wire  sprung  into  a 
groove  under  the  top  edge  of  the  wooden  case,  as  will  be 
seen  by  examining  the  instrument.  Connection  to  the  coil 
is  made  by  means  of  two  binding-posts  on  the  case,  shown 
at  a,b  in  Fig.  1017. 

When  the  instrument  is  used  as  a  tangent  galvanometer, 
the  case  containing  the  magnetized  needle  and  coil  is  placed 
within  the  circle  ^  on  a  cross  support  having  a  dowel  which 
fits  into  a  hole  in  the  center  of  the  case.  The  galvanometer 
may,  therefore,  be  turned  through  any  angle,  while  still 
keeping  the  magnetized  needle  in  the  center  of  the  large 
circle.  On  this  circle  are  wound  four  coils  of  two  turns 
each  of  No.  18  insulated 
wire,  and  the  ends  of 
these  coils  are  brought 
out  to  terminals  on  the 
base.  Thus,  the  ter- 
minals </,  d^  form  the 
ends  of  one  coil,  e,  e' 
are  the  terminals  for 
the  second  coil,  and  so 
on.  The  galvanometer 
should  be  so  placed 
within  the  coil  that  the 
scales  are  one  on  each 
side  of  the  circle.  When 
the    whole    instrument  fig.  1017. 

is  then  turned  so  that  the  glass  pointer  is  at  right  angles  to 
the  coil  and  over  the  zero  marks,  the  axis  of  the  magnetized 
needle  will  be  in  the  plane  of  the  coil. 

When  the  instruments  are  received,  they  should  be  care- 
fully unpacked  and  prepared  for  use. 

In  setting  up  the  galvanometer,  the  glass  cover  should 
first  be  removed  by  springing  out  the  brass  wire  ring  and 


1664  ELECTRICAL  MEASUREMENTS. 

introducing  a  thin  knife-blade  or  a  toothpick  under  the  edge 
of  the  glass.  The  cotton  which  is  placed  on  the  glass 
pointer  to  protect  it  while  in  transit  must  then  be  carefully- 
removed,  after  which  the  glass  should  be  replaced  and  the 
ring  sprung  in.     The  apparatus  is  then  ready  for  use. 

2536.  A  diagrammatic  representation  of  the  connec- 
tions of  the  bridge  for  ordinary  resistance  measurements  is 
shown  in  Fig.  1018.  From  this  it  will  be  seen  that  the  bat- 
tery B  (which  is  the  Leclanche  cell  already  furnished  the 
student)  is  connected  to  the  copper  contact  strips  to  which 


the  ends  of  the  slide  wire  are  also  fastened.  The  known 
resistance  R  and  the  unknown  resistance  X  are  connected 
between  the  outer  and  middle  strips. 

One  terminal  of  the  galvanometer  is  connected  to  the 
middle  strip  at  ^  by  a  wire  clamped  under  the  screw,  the 
other  terminal  being  connected  to  the  proper  point  on 
the  slide  wire  by  a  piece  of  insulated  wire  having  a  contact 
piece  at  the  end.  This  end  is  pressed  on  the  slide  wire  and 
moved  along  until  a  point  is  reached  where  alternately 
removing  it  from  and  touching  it  to  the  slide  wire  produces 
no  deflection  of  the  galvanometer.  With  care  in  observing 
that  the  galvanometer  needle  is  actually  not  deflected  even 
a  fraction  of  a  scale  division,  this  point  may  be  very  accu- 
rately located.  By  reading  the  number  of  the  division  on 
the  scale  at  this  point,  the  relation  between  the  lengths  of 


ELECTRICAL  MEASUREMENTS.  1665 

the  slide  wires  \^  «  and  na  may  be  readily  found,  and  the 
value  of  the  unknown  resistance  X  found  by  applying 
the  formula  given  in  Art.  2513,  but  substituting  the 
point  a  for  b  and  g  for  a^  as  these  letters  in  Fig.  1018  corre- 

spond  to  the  ends  of  the  wire  in  Fig.  1004,  X=  R — . 

ng 

For  example,  suppose  the  1-ohm  coil  to  be  used  as  R,  and 
that  the  position  of  the  point  n,  where  an  application  of  the 
galvanometer  lead  to  the  slide  wire  produces  no  deflection 
of  the  galvanometer,  to  be  opposite  division  415  on  the  scale 
starting  at  g\  this  will  be  the  third  division  from  the  line 
marked  400,  in  the  space  between.  400  and  450.  The  corre- 
sponding number  read  on  the  scale  which  starts  from  a  will 
be  585.  The  position  of  this  point  n  will  hereafter  be  called 
the  bridge  reading ;  in  this  case  the  bridge  reading  is  415  or 
585.  We  may  now  find  the  value  of  the  unknown  resistance 
X  by  the  formula  above, 

X=  IX???  =1.41  ohms. 
415 

The  accuracy   of  this  bridge  does  not  require  that  the 

results  be  carried  out  to  more  than  three  significant  figures. 

If  the  relative  position  of  X  and  R,  Fig.  1018,  be  reversed, 

the  formula  will  obviously  read  X=  R—^'     For  uniformity 

in  all  problems  given  in  this  section,  the  known  resistance 
will  be  considered  to  be  in  the  position  shown  in  Fig.  1018. 

In  using  the  detector  galvanometer,  see  that  it  rests  on  a 
level  surface,  so  that  the  needle  and  pointer  will  swing  clear. 
This  may  be  tested  by  causing  the  needle  to  deflect  (e.g.,  by 
momentarily  connecting  the  galvanometer  to  the  battery 
terminals),  first  in  one  direction  and  then  in  the  other;  the 
needle  should,  after  two  or  three  oscillations,  return  to  the 
same  position  from  either  side. 

When  using  the  tangent  galvanometer,  the  instrument 
may  be  leveled  by  means  of  the  three  leveling  screws  in  the 
base;  in  fact,  the  galvanometer  may,  for  most  purposes,  be 
kept  in  position  on  this  base. 


1666  ELECTRICAL  MEASUREMENTS. 

See  that  no  magnets  or  large  pieces  of  iron  are  near  the 
galvanometer,  or,  if  this  is  unavoidable,  see  that  the  relative 
position  of  the  galvanometer  and  the  magnets  or  pieces  of 
iron  is  not  changed  while  making  a  test. 

Set  the  galvanometer  up  in  such  a  position  that  the  ends 
of  the  pointer  coincide  with  the  zero  divisions  of  the  scale. 

If  either  the  pointer  or  pivot  is  not  exactly  central,  it  may 
be  that  each  end  will  not  coincide  with  the  zero  marks  at 
the  same  time.  If  this  is  the  case,  get  one  end  into  the 
proper  position  and  take  all  readings  from  that  end  of  the 
pointer. 

Do  not  rub  the  glass  cover  with  a  piece  of  cloth  or  paper 
before,  taking  a  reading,  as  the  static  charge  thus  induced 
on  the  glass  will  attract  the  glass  pointer,  thereby  causing 
it  to  indicate  incorrectly. 

In  making  all  experiments,  note  on  a  piece  of  paper  or  in 
a  note-book  the  apparatus  used,  and  how;  if  necessary, 
draw  a  diagram  of  connections,  etc.  Write  down  each 
result  as  soon  as  each  part  of  the  experiment  is  completed; 
do  not  trust  to  memory  for  results.  Make  all  experiments 
twice,  if  possible,  thus  checking  the  first  results.  By  taking 
the  above  precautions  and  exercising  care  in  taking  the 
readings,  reliable  and  instructive  results  may  be  obtained 
with  this  simple  apparatus  by  performing  the  experiments 
mentioned  in  the  succeeding  pages. 


EXPERIMENTS  "WITH  ELECTRICAL,  APPARATUS. 

Experiment  1. — As  stated  above,  one  of  the  resistance 
coils  has  1  ohm  resistance,  the  other  about  10.5  ohms.  It  is 
desirable  that  this  second  coil  have  10  ohms  resistance,  to 
facilitate  calculation,  etc.  The  process  of  winding  these 
coils  is  as  follows:  The  given  length  of  wire  is  cut  off  and 
folded  in  the  middle;  the  ends  are  then  soldered  to  the 
copper  terminals  and  the  doubled  wire  wound  on  the  spool, 
the  middle  of  the  length  of  the  wire  thus  coming  on  the 
outside  of  the  spool,  where  it  is  held  by  a  piece  of  thread. 
By  cutting  this  thread  the  middle  of  the  wire  is  released, 
and  a  length  may  be  unwound,  the  insulation  scraped  off, 


ELECTRICAL  MEASUREMENTS.  1667 

and  "the  two  bare  wires  firmly  twisted  together,  which  will 
have  the  effect  of  lessening  the  resistance  of  the  coil.  For 
this  experiment,  then, 

{a)  Find  the  resistance  of  the  fine  wire  resistance  coil, 
using  the  other  coil  as  the  standard,  and  calling  its  resist- 
ance 1  ohm. 

{d)  Figure  out  the  bridge  reading  which  would  result  if 
the  fine  wire  resistance  coil  were  of  10  ohms  resistance. 

[c)  Lessen  the  resistance  of  the  fine  wire  coil,  a  little  at 
a  time,  in  the  manner  described,  until  it  is  of  10  ohms  re- 
sistance.     State  the  various  steps  of 'the  operation  fully. 

{d)  From  the  results  of  experiment  (<:),  what  is  the 
total  length  of  wire  in  the  fine  wire  coil  as  furnished  ? 

Experiment  2. — Measure  off  about  40  feet  of  the  insu- 
lated wire  furnished  with  the  first  set  of  apparatus.  Con- 
nect this  in  the  place  of  the  unknown  resistance  Jf,  Fig. 
1018.  Use  the  1-ohm  coil  for  the  known  resistance  and 
measure  the  resistance  of  the  wire. 

(a)     What  is  the  resistance  per  foot  of  the  wire  ? 

(/?)  Assuming  it  to  be  pure  annealed  copper,  what  is 
the  diameter  of  the  wire,  calculated  from  the  above  meas- 
urement ? 

Experiment  3. — Connect  up  the  bridge,  battery,  and 
galvanometer  as  shown  in  Fig.  1019,  using  the  10-ohm  coil 
as  the  known  resistance  R.      It  will  be  seen  that  in  this  case 


Fig.  1019. 

the  galvanometer  takes  the  place  of  the  unknown  resistance, 
and  a  plain  wire  of  the  galvanometer  circuit,  in  the  ordinary 
method  of  connection.     (Fig.  1018.) 


1668  ELECTRICAL  MEASUREMENTS. 

When  the  connections  are  made,  a  current  will  flow 
through  the  galvanometer,  giving  a  certain  deflection.  If 
the  wire  that  takes  the  place  of  the  galvanometer  circuit  in 
the  ordinary  method  is  pressed  down  on  the  slide  wire  at 
any  other  point  than  where  no  current  passes  through  it, 
the  amount  of  current  in  the  circuit  will  be  changed  and  the 
deflection  of  the  galvanometer  will  correspondingly  change. 
Consequently,  if  a  point  on  the  slide  wire  is  found  where 
connecting  the  wire  produces  no  change  in  the  galvanometer 
deflection,  that  point  will  give  a  bridge  reading  from  which 
the  galvanometer  resistance  may  be  calculated  by  the  for- 
mula already  given. 

{a)  Perform  the  foregoing  experiment  and  calculate  the 
resistance  of  the  galvanometer. 

(<^)     Explain  the  theory  of  this  measurement. 

Experiment  4. — Scrape  the  insulation  ofif  one  end  of 
each  of  two  short  pieces  of  wire  for  about  6  inches.  Wrap 
the  bared  ends  firmly,  one  around  one  of  the  terminals  of 
the  10-ohm  coil  and  the  other  around  the  other  terminal, 
using  about  3  inches  of  the  bared  ends.  This  will  leave  3 
inches  or  so  projecting  from  each  terminal  (besides  the  in- 
sulated part),  which  should  be  connected  to  the  terminals  of 
the  galvanometer,  thus  connecting  the  10-ohm  coil  and  the 
galvanometer  in  parallel,  or,  in  other  words,  shunting  the 
galvanometer  with  the  10-ohm  coil. 

{a)  Calculate  the  combined  resistance  of  the  galvanometer 
and  its  shunt. 

{b)  Measure  this  combined  resistance  on  the  bridge  by 
the  method  described  in  Experiment  3,  using  the  1-ohm 
coil  for  the  known  resistance.  How  do  the  two  results  com- 
pare ? 

(r)     What  is  the  multiplying  power  of  this  shunt  ? 

Experiment  5. — Check  up  the  results  of  the  measure^ 
ments  given  in  Experiments  1  and  3  by  reversing  the  posi- 
tions of  the  known  resistance  and  the  unknown  resistance, 
using  the  modified  form  of  the  formula  as  given  in  Art 
2536.     How  do  the  results  compare  ? 


ELECTRICAL  MEASUREMENTS.  1669 

Experiment  6. — In  measuring  the  resistance  of  appara- 
tus located  at  some  distance  from  the  bridge,  it  is  necessary 
to  take  into  account  the  resistance  of  the  wires  leading  to 
the  resistance  that  is  to  be  measured.  This  can  best  be  done 
by  measuring  the  resistance  of  these  leads  separately,  their 
circuit  being  completed  by  twisting  or  pressing  the  distant 
ends  of  the  leads  together,  either  before  or  after  the  regular 
resistance  measurement  is  made,  and  deducting  this  resist- 
ance from  the  total  resistance  of  the  circuit  measured. 

Perform  this  experiment,  measuring  the  resistance  of  the 
1-ohm  coil  located  20  or  30  feet  away  from  the  bridge.  Use 
the  10-ohm  coil  as  the  standard,  and  some  of  the  wire  sup- 
plied with  the  first  lot  of  apparatus  for  the  leads.  Give  the 
total  resistance  of  the  circuit,  the  resistance  of  the  leads, 
and  the  resistance  of  the  coil. 

Experiment  7. — Secure  a  piece  of  the  carbon  from  an 
arc  lamp,  3  or  4  inches  long.  If  coated  with  copper,  scrape 
the  copper  off  or  eat  it  ofif  with  acid. 

(a)  Twist  the  bared  ends  of  two  short  pieces  of  wire 
around  the  carbon  at  points  as  near  the  ends  as  possible, 
and  measure  the  resistance  of  the  carbon  between  these  two 
points. 

[d)  Measure  carefully  the  diameter  of  the  carbon  and  the 
length  between  the  points  where  the  lead  wires  are  attached, 
and  from  these  figures  calculate  the  resistance  of  the  carbon 
for  an  inch  cube;  i.  e.,  what  would  be  the  resistance  of  a 
piece  of  the  carbon  experimented  upon  if  of  1  square  inch 
sectional  area  and  1  inch  long  ? 


SUGGESTIONS  FOR  EXPERIMENTS. 

2>S37,  If  the  student  has  access  to  an  electric-light 
station  he  can  measure  the  resistance  of  the  various  circuits 
of  the  dynamos  or  other  appliances,  or  of  the  lines,  at  times 
when  the  station  is  not  running,  or  can  measure  such  other 
resistances,  of  between. 05  and  200  ohms,  as  the  opportunity 
may  allow. 

Other  standard  resistances  may  be  prepared  on  the  same 
lines  as  those  furnished  with  a  bridge;  if  made  of  higher  or 


1670 


ELECTRICAL  MEASUREMENTS. 


lower  resistance  than  those  furnished,  they  will  increase  the 
range  of  resistances  that  may  be  measured,  although  accu- 
rate measurement  of  high  resistances  (500  ohms  or  over) 
should  not  be  expected. 

The  best  method  of  calibrating  the  tangent  galvanometer 
is  to  compare  it  with  a  standard  direct  reading  instrument — 
a  Weston  ammeter,  for  example.  If  this  can  not  readily  be 
done,  it  may  be  calibrated  by  the  copper  sulphate  electroly- 
sis method  described  in  Art.  2496  and  following.  The 
weight  measurements  should  be  carefully  made  on  a  delicate 
pair  of  scales.  Any  good  apothecary  has  such  a  pair  of 
scales,  and  would  probably  perform-  the  weighings  for  a 
small  sum. 

In  this  method  of  calibration,  copper  wires  may  be  sub- 
stituted for  the  copper  plates  described  in  Art.  2498,  they 
being  easier  to  clean  and  handle.  Two  wires  should  be  used, 
coiled  into  open  spirals,  one  about  twice  the  diameter  of  the 
other;  the  smaller  should  be  placed  inside  the  larger,  and 
connected  to  the  negative  pole  of  the  battery,  thereby  becom- 
ing the  electrode  to  be  weighed. 

Many  other  useful  applications  of  this  apparatus  which 
might  be  mentioned  will  occur  to  the  student  as  he  advances 
in  the  Course.  

PRACTICAL    MEASUREMENTS. 


INSTRUMENTS. 
2538.     Most  of  the  apparatus  and  tests  so  far  described 

are  more  for  laboratory 
use  than  for  the  shop  or 
station,  and  now  such 
accurate  and  reliable 
portable  measuring  in- 
struments are  made 
that  many  measure- 
ments before  referred 
to  may  be  made  with 
as  great  a  degree  of 
precision  and  much 
Fig.  1020.  greater     facility     than 


ELECTRICAL  MEASUREMENTS. 


1671 


with  the  various  galvanometers  and  other  apparatus  already 
described.      Some  of  the  best  forms  of  portable  instruments 


tiG.  1U21. 

made  are  those  known  as  the  Weston  instruments, 
general  form  is  shown 
in  Fig.  1020.  These 
instruments  are  made 
on  the  principle  of  the 
D'Arsonval  galvanom- 
eter (Art.  2476), 
as  shown  in  the  sec- 
tional view,  Fig. 
1021. 

Fig.  1022  shows  the 
magnetic  circuit  of 
this  form  of  instru- 
ment. The  permanent 
magnet  A  A  has  soft 
iron  pole-pieces  P,  P 
fastened  to  it  by  the 

m. 

screws  S,  S,  and  bored  Fig.  1023 


Theii 


1672 


ELECTRICAL  MEASUREMENTS. 


out  to  make  a  cylindrical  opening.  In  the  center  of  this  open- 
ing is  a  stationary  soft  iron  cylinder  C,  supported  in  place 
by  a  screw  J/ passing  through  a  lug  on  the  brass  plate  B. 
This  cylinder  being  of  less  diameter  than  the  opening 
through  the  pole-pieces,  there  is  left  a  narrow  gap  between 
the  pole-pieces  and  the  iron  core,  as  shown.  The  lines  of 
force  from  the  permanent  magnet  pass  across  this  space, 
making  a  strong  and  uniform  magnetic  field. 

The  movable  part  of  the  instrument  is  shown  in  Fig.  1023. 
It  consists  of  a  rectangular  coil  C  of  fine  wire  wound  on  an 


Fig.  loas. 
aluminum  or  thin  copper  bobbin,  which  is  suspended  verti- 
cally between  two  delicate  jeweled  bearings.  Two  flat 
horizontal  spiral  springs  5,  5  oppose  the  tendency  of  the 
coil  to  rotate,  and  at  the  same  time  conduct  the  current  to 
the  suspended  coil. 

A  thin  aluminum  pointer  P,  attached  at  right  angles  to 
the  coil,  moves  over  a  scale  and  indicates  the  deflection  of 
the  coil  from  its  normal  position,  which  is  as  shown  in  Fig. 
1021.  On  a  current  being  sent  through  the  coil  by  means 
of  the  springs  vS,  5,  there  is  a  tendency  for  the  coil  to  move 
through  the  magnetic  field  (Art.  2438),  which  it  will  do 
until  the  torsion  of  the  spiral  springs  equals  the  force  with 
which  the  coil  tends  to  move,  when  the  coil  will  come  to  rest, 
and  the  pointer  will  indicate  the  angle  of  deflection  of  the  coil. 

The  magnetic  field  being  practically  uniform,  the  angle  of 


ELECTRICAL  MEASUREMENTS.  1673 

deflection  is  closely  proportional  to  the  current  in  the  coil, 
so  the  scale  divisions  are  very  uniform,  as  is  shown  by  Fig. 
1024,  which  is  a  scale  about  three-fourths  size. 

The  copper  or  aluminum  bobbin  on  which  the  coil  is  wound, 
in  moving  through  the  magnetic  field,  has  an  electromotive 

60        70       80   _    90 

I   "JO 


Fig.  1024. 


force  set  up  in  it  which  causes  a  current  to  circulate  around 
the  bobbin  as  long  as  the  bobbin  moves.  This  current  cir- 
culates in  thie  opposite  direction  to  the  current  in  the  coil; 
hence,  it  tends  to  oppose  the  motion  of  the  coil.  As 
this  tendency  exists  only  when  the  bobbin  is  moving,  it 
has  the  effect  of  preventing  the  needle  from  swinging  too  far 
over  the  scale,  thus  bringing  it  quickly  to  rest  at  the  proper 
point. 

This  damping  effect  is  due  almost  entirely  to  the  currents 
in  the  bobbin.  The  friction  is  so  slight  that  it  has  practically 
no  effect  on  the  position  the  needle  will  take.  This  is  shown 
by  the  fact  that  the  needle  having  been  deflected  by  a  cur- 
rent will  respond  to  very  minute  variations  in  that  current; 
that  is,  the  instruments  are  very  sensitive. 

An  instrument  whose  moving  system  possesses  this  feature 
of  coming  to  rest  quickly  at  the  proper  point  is  known  as  a 
dead-beat  instrument ;  this  is  a  very  important  feature,  for  it 
assists  the  rapidity  of  taking  measurements  very  materially. 
The  moving  system  is  practically  the  same  for  all  direct-cur- 
rent Weston  ammeters  and  voltmeters.  If  the  instrument 
is  designed  for  a  voltmeter,  a  high  resistance,  located  in  the 
back  of  the  case,  is  connected  in  series  with  the  movable  coil; 
if  for  an  ammeter,  the  coil  is  connected  in  parallel  with  a 
short,  thick  piece  of  copper  or  some  alloy,  so  that  only  a 
small  part  of  the  current  passes  through  the  movable  coil, 
and  the  resistance  of  the  instrument  is  extremely  low.      By 


1674  ELECTRICAL  MEASUREMENTS. 

reason  of  this  extremely  low  resistance  of  the  ammeters  and 
the  high  resistance  of  the  voltmeters,  they  consume  very 
little  energy  indeed,  and  may  be  left  continuously  in  circuit 
without  undue  heating. 

For  example,  a  15-ampere  Weston  ammeter  has  an  internal 
resistance  of  .0022  ohm;  when  measuring  a  10-ampere  cur- 
rent, the  drop  (C  R)  is  .022  volt,  and  the  watts  expended 

(C  E)  =  .22,   or  about  one  thirty-four-hundredth  I  J  of 

a  horsepower. 

The  resistance  of  a  150-volt  voltmeter  is  about  19,000 
ohms.      Measuring    110  volts,   the    instrument    would    take 

=  .0058    ampere,     nearly,    with    a    consumption    of 

energy  of  .638  watt,  nearly,  or  about  of  a  horsepower. 

1,200 

The  conducting  parts  of  the  instrument  are  made  of  an 
alloy  having  a  very  low  temperature  coefficient,  so  that 
moderate  changes  in  the  temperature  of  the  instrument  do 
not  affect  its  readings  appreciably.  Beneath  the  needle  just 
inside  the  scale  is  a  mirror.  On  looking  down  on  the  needle, 
by  getting  the  needle  directly  over  its  reflection  in  the  mirror, 
errors  due  to  not  getting  the  needle  in  line  with  the  scale 
(known  as  parallax)  are  eliminated.  These  several  good 
features  make  these  instruments  very  reliable  and  convenient 
for  making  all  sorts  of  electrical  measurements,  and  as  they 
may  be  obtained  in  a  great  variety  of  ranges,  their  use  is 
very  general. 

There  are  many  other  forms  of  portable  instruments  made, 
most  of  them  being  constructed  on  the  same  general  principle 
as  the  Weston,  and  they  may  often  be  used  in  making  various 
measurements  to  good  advantage. 


SIEMENS   DYNAMOMETER. 

2539.  Another  instrument  which  is  largely  used  for 
measuring  currents  is  the  Siemens  dynamometer.  This  in- 
strument is  constructed  on  the  same  fundamental  principle 
that  the  Weston  and  many  other  electromagnetic  instru- 


ELECTRICAL  MEASUREMENTS. 


1675 


ments  are,  namely,  that  a  conductor  carrying  a  current  will 
tend  to  move,  if  in  a  magnetic  field,  with  the  direction  of  the 
lines  of  force  at  an  angle  to  the  direction  of  the  current. 

The  working  parts  of  this  instrument,  one  form  of  which 
is  shown  in  Fig.  1025,  consists  of  two  rectangular  coils  of 
wire,  one,  i%  fixed, 
the  other,  M,  mova- 
ble. The  normal  po- 
sition of  the  movable 
coil  is  with  its  plane 
at  right  angles  to  the 
plane  of  the  fixed 
coil,  and  it  is  sus- 
pended in  this  posi- 
tion by  a  fiber.  To 
the  top  of  the  coil  is 
also  attached  a  light 
helical  spring  S,  the 
other  end  of  which  is 
attached  to  a  milled 
nut  T.  On  turning 
this  nut  the  spring 
will     be      tightened,  Fig.  1025. 

thus  acting  to  move  the  coil. 

The  two  coils  are  connected  in  series,  connection  being 
made  to  the  movable  coil  by  means  of  mercury  cups  C,  C, 
into  which  the  ends  of  the  coil  dip. 

On  sending  a  current  through  the  two  coils  in  series,  the 
mutual  action  of  the  two  coils  tends  to  move  them  into  par- 
allel  planes.  The  effect  is  to  rotate  the  movable  coil  about 
its  vertical  axis;  by  turning  the  milled  nut,  a  tension  may 
be  put  on  the  spring  which  will  return  the  coil  to  its  origi- 
nal position.  The  force  exerted  by  the  spring  on  the  coil  is 
proportional  to  the  angle  through  which  the  milled  head 
attached  to  the  spring  is  turned;  so,  by  a  pointer  P,  at- 
tached  to  the  milled  head,  the  force  required  to  pull  the  coil 
back  to  its  central  position  may  be  indicated. 

A  pointer  /,  attached  to  the  movable  coil,  is  opposite  a 


rm=.^^ 

Hc^ 

r#r™=----^^^^""' 

?■  V  j 

1 

\/ 

V 

1676  ELECTRICAL  MEASUREMENTS. 

zero  mark  on  the  scale  when  the  movable  coil  is  at  right 
angles  to  the  fixed  coil. 

As  the  two  coils  are  in  series,  doubling  the  current  in  one 
coil  doubles  it  in  the  other,  so  the  mutual  force  of  both 
coils  is  doubled,  and  the  force  acting  on  the  movable  coil  is 
quadrupled ;  that  is,  the  force  on  the  movable  coil,  hence  the 
torsion  in  the  spring  necessary  to  bring  the  pointer  on  the 
coil  back  to  zero,  is  proportional  to  the  square  of  the  current. 

These  instruments  are  seldom  made  direct  reading,  but  are 
furnished  with  a  table  which  gives  the  deflections  corre- 
sponding to  various  current  strengths.  Intermediate  values 
may  be  interpolated  or  calculated. 

The  fixed  coil  is  usually  wound  in  two  parts  of  unequal 
number  of  turns  and  size  of  wire;  either  coil  may  be  used, 
thus  varying  the  range  of  the  instrument.  This  form  of  in- 
strument is  especially  useful,  as  it  may  be  used  equally  well 
for  alternating  current  as  for  direct,  since  there  is  no  iron  or 
other  magnetic  material  used  in  its  construction. 


EDISON   CHEMICAL.    METER. 

2540.  As  stated,  most  of  the  measuring  instruments  in 
commercial  use  depend  on  the  electromagnetic  effect  of  a 
current  for  their  action;  perhaps  the  only  electrochemical 
current  meter  that  is  in  commercial  use  is  the  Edison  chem- 
ical meter,  which  is  extensively  used  by  the  Edison  Illumi- 
nating Companies.  In  this  instrument  a  fixed  proportion  of 
the  current  passing  through  the  meter  is  shunted  through 
an  electrolytic  bath  consisting  of  two  zinc  plates  dipping  in 
a  solution  of  sulphate  of  zinc.  The  plates,  solution,  and  con- 
nectors are  all  mounted  in  little  glass  jars,  and  two  jars  are 
set  up  in  each  meter,  one  to  act  as  a  check  on  the  other. 
At  the  end  of  a  certain  fixed  time  (usually  thirty  days)  the 
jars  and  their  contents  are  replaced  by  others,  and  the  am- 
pere-hours of  current  that  have  been  used  by  the  customer 
calculated  from  the  gain  in  weight  of  the  negative  plate. 
By  various  ingenious  devices  in  the  several  parts  of  the 
meter,  the  effects  of  various   sources  of  error   are   almost 


ELECTRICAL  MEASUREMENTS. 


1677 


entirely  removed.     Great  care,  however,  must  be  exercised 
in  removing  the  jars  and  caring  for  their  contents.      Fig. 


Fig.  1026. 

1026   gives  a  view  of  the  latest   type  of   Edison  chemical 
meter. 


CARDEIV    VOLTMETER. 

2541.  The  representative  instrument  of  the  class  that 
measures  the  heating  effect  of  the  current  is  the  Cardew 
voltmeter,  illustrated  in  Fig.  1027. 

In  this  instrument  a  long  wire  w,  usually  of  some  platinum 
alloy,  is  stretched  from  end  to  end  of  the  long  tube  a  ;  each 
end  is  fastened  to  the  dial  end  of  the  tube ;  the  wire  then 
passes  over  pulleys  at  the  end  of  the  tube  and  back  to  the 
dial  end,  where  a  spring  attached  to  the  middle  of  the  wire 
keeps  it  stretched  taut.  On  a  current  being  sent  through 
the  wire,   the   heat   caused   by  the  passage  of  the  current 


1678 


ELECTRICAL  MEASUREMENTS. 


expands  the  wire;  the  addition  to  its  length  is  taken  up  by 
the  spring-,  and  the  motion  of  the  middle  of  the  wire  which 
is  attached  to  the  spring  is  transmitted  to  a 
needle  b  by  suitable  multiplying  gear,  so  that 
the  motion  of  the  needle  over  the  dial  is  a 
measure  of  the  amount  of  expansion  of  the 
wire. 

The  wire  is  usually  of  small  diameter  and 
considerable  specific  resistance,  so  that  it  in 
itself  has  resistance  enough  to  allow  the  in- 
strument to  be  used  as  a  voltmeter  for  poten- 
tials less  than  about  100  volts  without  external 
resistance.  This  voltmeter  may  be  used  either 
for  alternating  or  direct  currents,  is  remark- 
ably dead-beat,  and  simple  in  construction.  Its 
internal  resistance  is  low  for  a  voltmeter,  and, 
in  consequence,  it  takes  considerable  current, 
enough  in  many  instances  to  seriously  affect 
some  conditions  of  an  experiment.  This  in- 
strument has  no  particular  law  of  deflections 
FIG.  1027.  by  which  the  scale  is  divided;  the  principal  di- 
visions are  determined  by  comparing  the  instrument  with  a 
standard,  and  the  intermediate  divisions  interpolated. 

There  are  several  other  instruments  made  on  this  prin- 
ciple, commonly  known  as  hot-wire  instruments  ;  the  Cardew 
is  the  best  known. 


^w 


"WATTMETERS. 

2542.  The  energy  expended  in  a  circuit  being  the 
product  of  the  current  and  the  electromotive  force,  these 
factors  may  be  measured  separately,  and  multiplied  together 
to  obtain  the  number  of  watts  expended.  Instruments  have 
been  designed,  however,  which  automatically  perform  this 
multiplication,  thus  measuring  watts  directly,  one  of  the 
best  known  being  the  Siemens  wattmeter. 

This  instrument  is  of  the  same  general  form  as  the 
current-meter,  Fig.  1025,  the  difference  between  the  instru- 
ments being  that  in   the  wattmeter  the  two  coils  are  not 


ELECTRICAL  MEASUREMENTS. 


1679 


consequently    the    total 


Fig.  1028. 


in  series.  This  instrument  measures  at  all  times  the  product 
of  the  current  in  any  circuit  and  the  difference  of  potential 
between  the  ends  of  that  circuit.  The  stationary  coil  is  in 
series  with  the  outside  circuit: 
current  flows  through 
it.  The  movable  coil 
is  in  series  with  a  resist- 
ance great  enough  to 
prevent  the  full  differ- 
ence of  potential  be- 
tween the  mains  send- 
ing more  than  a  small 
amount    of    current  ^ 

through     the     movable     (S(S?)(^  d 

coil.  This  coil  and  the 
resistance  are  then  con- 
nected in  parallel  with  the  rest  of  the  circuit,  as  shown  in 
Fig.  1028,  where  F  is  the  fixed  coil  of  the  instrument;  J/, 
the  movable  coil;  7?,  the  resistance  that  is  connected  in 
series  with  M\  D,  the  source  of  electricity,  and  C  the;  exter- 
nal circuit,  the  energy  expended  in  which  it  is  desired  to 
measure. 

It  is  evident  that  if  the  drop  in  volts  through  the  circuit 
C  be  constant,  the  current  through  M  will  also  be  constant. 
The  force  acting  on  the  movable  coil  will  then  vary 
directly  as  the  current  in  the  coil  F;  the  potential  being 
constant,  the  watts  expended  in  the  circuit  will  also  vary 
directly  as  the  current.  If  the  current  in  the  coil  F  is 
constant,  variations  in  the  E.  M.  F.  will  vary  the  current  in 
the  coil  M  in  the  same  proportion,  and  the  force  on  the  coil 
71/ will  then  vary  directly  as  the  E.  M.  F. ;  the  current  in  the 
circuit  C  being  constant,  the  watts  will  also  vary  directly  as 
the  E.  M.  F.  So,  in  either  case,  the  force  acting  on  the 
movable  coil  (consequently  the  force  required  to  bring  it  to 
zero  position)  varies  directly  as  the  watts.  When  varia- 
tions occur  in  both  current  and  potential  simultaneously, 
the  same  holds  true,  and  the  force  required  to  bring  the  coil 
to  the  zero  position  is  proportional  to  the  watts. 


1680  ELECTRICAL  MEASUREMENTS. 

The  general  appearance  of  the  wattmeter  is  almost  pre- 
cisely the  same  as  that  of  the  current  dynamometer.  The 
resistance  used  with  the  movable  coil  is  usually  made  a. 
separate  piece  of  apparatus;  when  made  so  that  it  has  no 
self-induction^  the  wattmeter  may  be  used  for  measuring 
the  energy  expended  in  alternating-current  circuits. 


THE  THOMSON  RECORDING   WATTMETER. 

2543.  The  Siemens  wattmeter  gives  the  instantaneous 
value  of  the  watts  expended  in  the  circuit.  The  Thomson 
wattmeter  is,  as  its  name  indicates,  a  recording  meter,  and 
its  readings  give  the  product  of  the  watts  and  time,  i.  e., 
the  watt-hours.  The  construction  is  simple;  the  principle 
is,  broadly,  that  of  the  Siemens  dynamometer.  The  movable 
coil  is  not  held  to  zero  position,  but  revolves,  and  does  not 
surround  the  fixed  coil,  but  revolves  between  two  fixed  coils. 
The  movable  coil  is  really  a  small  drum-wound  armature^ 
provided  with  a  small  coinmutator  made  of  silver  to  prevent 
oxidation.  The  effect  of  using  the  commutator  is  to  make 
the  effective  plane  of  the  coil  (armature)  take  a  position  at 
right  angles  to  the  plane  of  the  fixed  coils. 

The  connections  of  this  instrument  are  made  on  the  same 
principle  as  those  of  the  Siemens  wattmeter.  The  fixed 
coils  are  in  series  with  the  circuit,  and  the  movable  coil  and 
a  resistance  in  series  with  it  are  in  parallel  with  the  circuit. 

The  amount  of  energy  expended  in  the  circuit  is  measured 
by  the  rotation  of  the  movable  coil,  a  worm  on  the  shaft  on 
which  the  movable  coil  is  mounted  engaging  with  a  set  of 
gears  which  operate  a  dial  similar  to  a  gas-meter  dial,  so 
that  the  energy  expended  in  a  certain  given  time  in  the  cir- 
cuit may  be  read  directly  from  the  dial  in  watt-hours. 

The  friction  of  the  apparatus  being  exceedingly  small, 
the  retarding  force  on  the  coil  that  opposes  its  tendency  to 
rotate  is  imparted  by  a  thin  copper  disk  attached  to  the 
shaft  on  which  the  movable  coil  is  mounted.  This  disk  is 
rotated  between  the  poles  of  strong  permanent  magnets; 
the  lines  of  force  from  the  magnets  cutting  the  disk  set  up 
electromotive  forces  between  adjacent  points  on  the  disk; 


ELECTRICAL  MEASUREMENTS. 


1681 


the  disk  being  of  copper,  the  resistance  between  those  points 
is  very  low,  so  that  a  considerable  current  may  flow.  This 
current  tends  to  retard  the  rotation  of  the  copper  disk,  and 
this  tendency  increases  directly  as  the  speed.  As  in  the 
Siemens  wattmeter,  the  force  acting  to  rotate  the  movable 


Fig.  1029. 

coil  increases  directly  as  the  watts;  therefore,  the  number 
of  revolutions  of  the  moving  system  of  the  meter  will  be 
directly  proportional  to  the  watts  expended  in  the  circuit; 
This  meter  may  be  used  for  either  alternating  or  direct  cur- 
rents, and  gives  very  accurate  results.  Fig.  1029  represents 
the  Thomson  meter  with  the  cover  removed. 


SH ALLEN BERGER   METER. 

2544.  This  meter  is  constructed  on  a  similar  principle 
to  the  Thomson  meter,  but  is  designed  to  be  used  only  on 
alternating-current  circuits,  as  is  also  the  Duncan  meter. 
Other  recording  meters  are  in  use,  but  are  usually  compli- 
cated in  construction  and  rather  unreliable  in   operation. 


1682  ELECTRICAL  MEASUREMENTS. 

In  addition  to  the  Siemens  wattmeter,  there  have  recently 
been  introduced  general  forms  of  portable  direct-reading 
wattmeters,  which  are  giving  good  satisfaction,  and  are 
more  convenient  to  use  than  the  Siemens  form. 


SWITCHBOARD  INSTRUMEIVTS. 
2545.  In  lighting  and  power  stations  and  similar  places, 
it  is  often  desirable  to  know  the  approximate  number  of 
amperes,  volts,  or  watts  delivered  by  a  machine  or  machines, 
and  for  this  purpose  instruments  have  come  into  use  which, 
while  not  sufficiently  accurate  for  making  reliable  measure- 
ments to  a  great  degree  of  precision,  are  very  useful  in 
indicating  approximately  the  output  of  a  machine  or  the 
load  on  a  circuit.  The  scales  of  such  instruments  are 
usually  large  and  open,  so  they  may  be  read  from  a  dis- 
tance. Many  forms  of  such  instruments  are  made  by 
different  manufacturers ;  their  principle  of  operation  is  usu- 
ally the  electromagnetic  effect  of  the  current,  but  their  de- 
tails of  construction  will  not  be  described  here. 


MEASUREMENTS  WITH  COMMERCIAL 
INSTRUMENTS. 

2546.  Most  of  the  measurements  previously  described 
as  being  made  with  some  form  of  galvanometer  can  be 
made  with  good  commercial  instruments — the  Weston,  for 
example. 

In  the  Weston  instruments,  the  terminals  of  the  ammeter 
are  both  on  the  same  (right)  side  of  the  instrument  (see 
Fig.  1020),  and  are  made  large  and  heavy,  while  in  the  volt- 
meters the  terminals  are  on  opposite  sides,  are  made  small, 
and  are  usually  covered  with  rubber,  in  order  that  they 
may  be  handled  without  danger  from  shocks.  Some  of  the 
voltmeters  are  made  with  the  resistance  coils  in  two  sec- 
tions, of  such  relative  value  that,  when  only  one  section  is 
in  circuit,  the  scale  readings  are  some  convenient  submulti- 
ple  of  the  readings  when  both  sections  are  used.  In  this 
case  the  instrument  is  provided  with  an  extra  binding-post 


ELECTRICAL  MEASUREMENTS. 


1683 


on  the  left  side,  and  the  scale  divisions  have  two  values; 
for  instance,  the  voltmeter  with  a  range  of  150  volts  may- 
have  the  resistance  so  divided  that  by  using  the  third  bind- 
ing-post the  range  will  be  15  volts  and  the  scale  divisions 
will  have  yV  their  former  value. 

Measurements  of  current  strength  or  difference  of  poten- 
tial are  very  simple.  To  measure  the 
number  of  amperes  flowing  in  a  circuit,  it 
is  only  necessary  to  connect  an  ammeter 
of  proper  capacity  in  series  with  the  rest 
of  the  circuit,  as  shown  in  Fig.  1030,  and 
read  the  amperes  directly  from  the  posi- 
tion of  the  pointer  on  the  scale.  The 
resistance    of    the    ammeter,    as    pointed  fig.  io30. 

out,  is  so  low  that  it  will  not  affect  the  total  resistance  of 
the  circuit  appreciably.  The  difference  of 
potential  between  two  points  in  a  circuit, 
or  the  E.  M.  F.  of  a  battery,  or  other  source 
of  E.  M.  F.,  may  be  readily  measured  by 
connecting  the  terminals  of  a  voltmeter  to 
the  proper  points  of  the  circuit  and  read- 
ing the  voltage  direct,  as  shown  in  Fig. 
1031. 

By  using  instruments  of  the  proper  range,  very  low  or 
very  high  resistances 
may  be  measured. 
Fig.  1032  shows  a 
way  of  measuring  a 
very  low  resistance — 
in  this  case  a  section 
of  copper  rod.  Here 
a  current  from  the  bat- 
tery B,  measured  by 
the  ammeter  A,  flows 
through  the  section  of 
copper  rod  R,  and  the 
drop  between  the 
points     C    and    D    is  fig.  1032. 


1684 


ELECTRICAL  MEASUREMENTS. 


measured  by  the  voltmeter  V.  As  the  drop  through  a 
short  section  of  copper  rod  would  be  very  slight,  except  with 
an  enormous  current,  a  voltmeter  capable  of  measuring 
very  small  differences  of  potential  must  be  used.  They  may 
be  had  to  measure  from  0  to  ,05  volt,  such  an  instrument 
being  known  as  a  millivoltmeter. 

Example. — If,  in  the  above  figure,  the  reading  of  the  ammeter  be 
34.5  amperes,  and  that  of  the  millivoltmeter  be  .00875  volt,  what  is  the 
resistance  of  the  copper  rod  between  C  and  B  ? 
.00875 


Solution. — 


-=f 


35.4 


=  .000247  ohm.     Ans. 


J5i 


ls>    ^ 


r.M. 


\-^I\I\l\ 


'l/WW 


High  resistances  may  be  measured  in  a  similar  manner  by 
using  a  low-reading  ammeter  (mil-ammeter)  and  a  high- 
reading  voltmeter.  The  high-reading  voltmeters  may  also 
be  used  to  measure  very  high  resistances,  such  as  insulation 
I  I  I  I  resistances;  the  method  of 

connecting  up  for  such  a 
test  is  shown  in  Fig.  1033. 
Here  jI^  is  the  insulation  to 
be  measured,  B  C  a.  battery 
or  other  source  of  E.  M.  F., 
which  should  be  as  high  as 
convenient,  as  long  as  it  is 
within  the  range  of  the  in- 
strument, V  M  the  volt- 
meter, and  K  a  switch  for 
shunting  the  resistance  R.  As  the  resistance  of  the  switch 
K  is  practically  nothing,  it  is  evident  that  when  it  is  closed 
the  voltmeter  is  connected  directly  to  the  terminals  of  the 
battery  and  will  measure  its  E.  M.  F.,  and  when  the  switch 
K  is  open  the  resistance  R  is  in  series  with  the  voltmeter. 
The  formula  for  finding  the  value  of  R  in  ohms  is 

R  =  r{^-lS^,  (466,) 

where  d  =■  deflection  of  voltmeter  with  the  resistance  R  not 
in  circuit,  d^  =  deflection  of  voltmeter  with  resistance  R  in 
circuit,  and  r  -•.  resistance  of  voltmeter. 

This  formula  is  obtained  as  follows:     The  E.  M.  F.  of  the 


Pig.  1033. 


ELECTRICAL  MEASUREMENTS.  1685 

battery  B  C  being  constant,  the  drop  through  the  voltmeter 
only  or  the  voltmeter  and  resistance  in  series  will  be  the 
same,  that  is,  C r  =  C^R-\-  C^  r. 

As  the  deflection  of  the  voltmeter  needle  is  proportional 
to  the  current,  this  may  be  written 

dr  =  d^R-[-  d^r\ 
or,  dr  —  d^r  =  d^R\ 

dr      d^r       „ 

dr  jy 


hence,  ^\~^ — l)=-^» 


which  is  the  formula  given. 

In  the  simple  case  where  the  resistance  to  be  measured  is 
just  equal  to  the  voltmeter  resistance,  it  is  evident  that  the 
deflection  of  the  voltmeter  with  the  resistance  in  series 
with  it  would  be  half  that  when  the  voltmeter  alone  is  in 
circuit,  which  satisfies  the  equation  as  follows: 

Given,  rX{\  —  l)=R. 

Then,  rxl=Ry 

and  r  =  R. 

Example. — If  the  E.  M.  F.  of  the  battery,  as  measured  by  the  volt- 
meter, is  100  volts,  and  the  deflection,  when  the  resistance  to  be 
measured  is  in  circuit,  is  40  volts,  what  is  the  value  of  that  resistance 
in  ohms  if  the  resistance  of  the  voltmeter  is  18,000  ohms  ? 

Solution.— In  this  case  ^=100,  di  =  40,  r=  18,000.  Then,  by 
formula  466, 

J?  =  18,000(^3:7-  _  1)  =  18,000  X  1.5  =  27,000  ohms.     Ans. 

2547.  It  will  be  seen  that  this  method  of  testing  insula- 
tion is  on  exactly  the  same  principle  as  that  shown  in  Fig. 
1008  (Art.  2522),  the  known  resistance  in  this  case  being 
that  of  the  instrument  itself.  Slight  variations  in  the 
E.  M.  F.  of  the  source  of  supply  do  not  afifect  the  result 
very  materially,  and  when  an  approximately  constant  known 
E.  M.  F.  is  available,  such  as  an  electric-lighting  circuit,  in- 
sulation tests  may  be  made  with  great  facility  by  merely 
connecting  the  voltmeter  in  series  with  the  E.  M.  F.  and 


1686 


ELECTRICAL  MEASUREMENTS. 


the    insulation    resistance.       On    the    assumption    that   the 
E.  M.  F.  has  a    constant  (known)    value,    a   table  may    be 

prepared  showing  the  insula- 
tion resistance  corresponding 
to  various  deflections  of  the 
voltmeter. 

This  affords  a  ready  means 
of  testing  the  insulation  resist- 
ance of  lighting  circuits  where 
the  E.  M.  F.  of  the  dynamos 
is  constant,  if  the  voltmeter 
is  of  high  resistance;  by  con- 
necting the  voltmeter  be- 
tween one  side  of  the  circuit  and  the  ground,  the  deflection 
of  the  needle  will  give  the  insulation  resistance  of  the  otJier 
side  of  the  line,  or  will  show  the  presence  of  a  "ground," 
as  represented  in  Fig.  1034.  Both  sides  may  be  tested  in  this 
manner,  and  it  is  usual  to  provide  a  small  switch  or  other 
convenient  apparatus  for  readily  making  the  desired  con- 
nections. 


Fig.  1034. 


Fig.  1035. 


2548.     For  many  electrical  measurements,  it  is  neces- 
sary to  know  the  rate  of  revolution  of  certain  moving  parts 


ELECTRICAL  MEASUREMENTS. 


1687 


Fig.  1036. 


of  machinery.  The  number 
of  revolutions  made  by  the 
machinery  in  one  minute  or 
other  length  of  time  does  not 
necessarily  give  its  rate  of 
revolution,  so  that  for  ac- 
curate work  the  ordinary 
revolution  counter  is  scarcely 
suitable.  Instruments  called 
tachometers  are  made 
which  indicate  by  the  posi- 
tion of  a  needle  on  a  dial  the 
rate  of  revolution  of  the  ap- 
paratus to  which  they  are 
connected.  The  principle  of 
these  instruments  is  similar 
to  that  of  a  centrifugal  en- 
gine governor;  two  weights 
are  thrown  out  from  their 
center  of  rotation  by  centrif- 
ugal force,  and  their  ten- 
dency to  move  is  overcome 
by  a  spring.  By  suitable 
gearing  the  motion  of  the 
weights  is  made  to  actuate 
a  pointer  which  moves  over 
a  suitably  divided  dial,  thus 
indicating  the  rate  of  rota- 
tion of  the  weights. 

Fig.  1035  shows  a  form  of 
tachometer  which,  being 
belted  to  a  pulley  of  suitable 
diameter  by  a  light  belt,  will 
give  the  rate  of  revolution  of 
that  pulley. 

The  form  shown  in  Fig. 
1036  is  intended  to  hold  in 
the    hands.      A    three-sided 


1688  ELECTRICAL  MEASUREMENTS. 

point  on  one  of  the  spindles  of  the  instrument  is  intended  to 
be  thrust  into  the  center  mark  of  a  revolving  shaft,  when 
the  rate  of  revolution  of  that  shaft  is  indicated  on  the  dial. 
It  is  usual  to  make  three  little  ridges  in  the  sloping  sides  of 
the  center  mark  of  the  shaft  with  a  three-sided  punch  (sup- 
plied with  the  instrument),  to  insure  that  the  point  on  the 
tachometer  shaft  will  not  slip  when  the  instrument  is 
applied. 

2549.  Electrical  measurements  may  be  broadly  stated 
to  be  measurement  of  current.  The  principal  methods  of 
measuring  current  and  their  general  applications  have  been 
described,  but  for  particular  cases  these  methods  often 
require  much  modification  in  detail,  and  to  arrive  at  cer- 
tain results  many  combinations  of  such  methods  may  be 
made,  according  to  the  requirements  of  the  case  in  hand. 
Some  of  these  combinations  and  modifications  for  special 
cases  will  be  described  where  necessary  in  succeeding  sections. 


BATTERIES. 


DEFINITIONS. 

2550.  An  electric  battery  is  a  combination  of  a  num- 
ber of  separate  electric  sources.  Thus,  a  voltaic  or  galvanic 
battery  (see  Arts.  2238  and  2239)  is  a  combination  of  a 
number  of  separate  voltaic  cells  properly  joined  together. 

The  term  battery  is  also  applied  to  a  combination  of 
Leyden  jars  (see  Art.  2232)  properly  joined  together  so 
as  to  form  a  so-called  Leyden  battery.  A  battery  of  this 
kind,  however,  has  very  little  practical  value,  in  the  present 
state  of  the  art,  compared  to  the  value  of  the  two  great 
classes  of  batteries  treated  of  in  this  discussion,  namely: 

I.      Primary  batteries. 
II.      Secondary     or     storage     batteries,     sometimes 
called  accumulators. 

255 1 .  A  primary  battery  is  a  combination  of  a  num- 
ber of  primary  cells  so  as  to  form  a  single  source. 

2552.  A  secondary  or  storage  battery  is  a  com- 
bination of  a  number  of  secondary  cells  so  as  to  form  a 
single  electric  source. 

2553.  Primary  batteries,  as  well  as  secondary  batteries, 
depend  for  their  operation  upon  the  chemical  action  which 
takes  place  between  certain  different  substances  when 
brought  into  contact  with  each  other.  The  whole  theory 
and  operation  of  cells  and  batteries  being  thus  dependent 
on  chemical  action,  it  is  necessary  to  give  here  some  prin- 
ciples of  chemistry,  which  is  that  science  which  treats  of 
the  composition  of  matter,  of  the  changes  produced  therein 
by  the  action  of  heat  and  other  natural  forces,  and  of  the 
action  and  reaction  of  different  kinds  of  matter  upon  each 
Other. 

For  notice  of  copyright,  see  page  imnaediately  following  the  title  page. 


1690  BATTERIES. 

PRINCIPLES  OF  CHEMISTRY. 

2554.  Chemical  action  is  that  which  produces  a 
change  in  the  chemical  condition  of  matter,  and  may  be 
action  of  decomposition,  i.  e.,  spHtting  a  substance  up 
into  other  distinct  substances;  or  action  of  recomposition, 
i.  e. ,  uniting  two  or  more  different  substances  into  a  new  one. 

2555.  Decomposition  can  not  go  on  indefinitely;  if  a 
substance  be  split  up  by  decomposition,  and  the  resulting 
substances  (if  possible)  be  again  split  up,  and  so  on,  a  point 
will  be  reached  where  substances  are  found  which  by  no 
known  process  can  be  further  decomposed.  Such  substances 
are  called  elements. 

2556.  A  chemical  compound  is  the  union  of  two  or 
more  elements  to  form  a  new  substance.  Compounds  may 
be  formed  by  the  union  of  two  or  more  compounds;  but  this 
is  merely  a  new  union  of  the  elements  which  originally  formed 
the  uniting  compounds. 

2557.  There  have  so  far  been  discovered  about  seventy- 
two  substances  which  seem  to  be  elements.  About  half  of 
these  are  very  rare ;  the  balance,  the  more  important,  are 
given  in  Table  89.  To  prevent  constant  repetitions  of  their 
names,  and  to  aid  in  expressing  the  composition  of  sub- 
stances, there  has  been  assigned  to  each  element  a  symbol^ 
consisting  of  the  initial  letter,  or  the  initial  letter  and  another 
letter  of  its  Latin  name,  which  is  often  different  from  its  com- 
njon  name.     These  symbols  are  given  in  column  2,  Table  89. 

2558.  The  exact  nature  of  chemical  action  is  not  known, 
any  more  than  is  the  exact  nature  of  electricity  or  heat;  but 
it  is  similar  to  other  physical  phenomena  in  that  chemical 
action  is  a  manifestation  of  energy.  This  energy  is  appar- 
ently stored  up  in  the  atoms  of  the  elements  2^^  potential 
energy,  and  causes  such  atoms  to  have  an  affinity  for,  or 
tendency  to  combine  with,  other  atoms,  this  affinity  being 
greater  or  less  according  to  the  relative  amount  of  potential 
energy  stored  in  the  combining  atoms.  Under  the  proper 
conditions,    these   affinities   cause   the   atoms   to   combine, 


BATTERIES.  1691 

which  allows  their  potential  energy  to  appear  as  kinetic 
energy,  usually  in  the  form  of  heat.  Thus,  chemical  com- 
bination develops  kinetic  energy,  while  to  perform  chemical 
decomposition,  kinetic  energy  must  be  supplied. 

2559.  The  heat  given  out  by  the  formation  of  a  com- 
pound is  known  as  the  heat  of  formation  of  that  substance. 
The  amount  of  this  heat  has  been  measured  in  the  case  of 
some  substances,  and  tables  giving  these  values  are  published 
in  most  works  on  chemistry. 

Note. — The  heat  of  formation  is  usually  expressed  in  calories  (per 
gram  of  the  substance),  the  calorie  used  being  the  lesser,  or  grain- 
degree,  calorie  which  is  the  heat  required  to  raise  1  gram  of  water 
1°  C.     It  is  obviously  .001  of  the  calorie  defined  in  Art.   1 130. 

2560.  An  element  is  the  ultimate  substance  to  which 
any  compound  can  be  chemically  subdivided.  As  has  been 
explained  in  Art.  1089,  all  matter  (every  substance)  is 
(mechanically)  composed  of  molecules,  they  being  the  small- 
est/(:zr//<:/^.s'  into  which  the  substance  can  be  mechanically 
subdivided  without  being  resolved  into  its  elements.  The 
molecules  are  each  made  up  of  a  number  of  atoms  of  the 
elements  of  which  the  substance  is  composed,  and  in  any 
given  substance  each  molecule  is  always  composed  of  the 
saine  total  member  of  atoms  of  its  elements  combined  in  the 
same  proportions;  if  the  proportionate  number  of  atoms  of 
any  element  is  changed,  a  new  substance  is  formed.  When 
an  element  exists  uncombined,  its  atoms  do  not  exist  alone, 
but  group  together  into  molecules,  just  as  the  atoms  of  the 
different  elements  group  together  to  form  the  molecules  of 
the  compound. 

2561.  By  very  careful  analysis  and  measurement,  it 
has  been  determined  that  elements  always  combine  in  certain 
fixed  proportions  or  multiples  of  those  proportions;  from  this 
fact,  it  is  possible  to  assign  to  each  element  a  number, 
which  number,  or  a  multiple  of  it,  will  represent  the  propor- 
tion, by  weight,  of  that  element  which  enters  into  any  com- 
pound. To  this  number  is  assigned  the  name  atomic 
weight,  and  these  numbers  represent  the  relative  rveights 


1692 


BATTERIES. 


of  the  atoms  of  the  elements.     The  actual  weight  of  an  atom 
has  been  calculated,  but  is  unimportant  here. 

Hydrogen  being  the  lightest  of  the  elements,  the  weight 
of  its  atom  is  taken  as  the  unit,  and  the  atomic  weights 
of  all  other  elements  calculated  therefrom.  The  atomic 
weights  of  the  more  common  elements  will  be  found  in  col- 
umn 3  of  Table  89. 

TABLE  89. 

THE  PRINCIPAL   ELEMENTS. 


Name  of  Element. 


Aluminum 
Antimony- 
Arsenic  .. . 
Barium.  . , 
Bismuth  . . 
Boron  .... 

Bromine . . 

Cadmium. 
Calcium.. . 
Carbon  . . . 

Chlorine . , 
Chromium 
Cobalt  . . . 
Copper.. . . 
Fluorine  . . 

Gold 

Hydrogen  . 


Sym- 
bol. 


Al 
Sb 
As 
Ba 
Bi 
B 

Br 

Cd 
Ca 


Atomic 
Weight. 


27.00 
120.00 

75.00 
137.00 
208.90 

11.00 

79-95 

112.00 
40.00 


t 

12.00 

CI 

35-45 

Cr 

52.10 

Co 

59.00 

Cu 

63.40 

Fl 

19.00 

An 

197.30 

H 

1. 00 

Valency. 


Ill 

V 
V 

II 

V 

III 
I 

VII 

II 
II 

IV 

I 

VII 

II 

VI 

i  n 

^  VIII 

i  I 
(  II 

I 

VII 

j  I 

I  III 

I 


Chemical 
Equiva- 
lent. 


9.00 
24.00 
15.00 
68.50 
41-78 

3.66 

79-95 
11.42 

56.00 

20.00 

3.00 

35-45 

5-07 

26.05 

7-44 
29.50 

7-38 
63.40 
31.70 
19.00 

2.57 
197.30 

65-77 


Electro- 
chemical 
Equivalent. 
Grams  per 
Coulomb. 


.00009324 
.00024860 
.00015540 
.00070960 
.00043280 
.00003792 
.00082100 
.00011840 
.00058020 
.00020720 
.00003098 
.00036730 
.00005252 
.00026990 
.00007708 
.00030560 
.00007646 
.00065680 
.00032840 
.00019680 
.00002663 
.00204400 
.00068140 
.00001036 


BATTERIES. 


1693 


TABLE  89 — Continued. 


Name  of  Element. 


Sym- 
bol. 


Atomic 
Weight. 


Valencv. 


Chemical 
Equiva- 
lent. 


6. 

Electro- 
chemical 

Equivalent. 

Grams  per 
Coulomb. 


Iodine. 
Iron  . 


Lead 

Magnesium 
Manganese. 


Mercury , 


Nickel  .... 
Nitrogen. . . 
Oxygen .... 
Phosphorus 
Platinum.. . 
Potassium.. 
Selenium. . . 


Silicon. . . . 

Silver 

Sodium  .. . 
Strontium. 

Sulphur  . . 

Telluriufn 

Tin 

Zinc 


Fe 

Pb 

Mg 
Mn 

Her 


Si 

Ag 

Na 
Sr 


125-85 
56.00 

206.95 
24.30 


Ni 

58.00 

N 

14.03 

0 

16.00 

P 

31.00 

Pt 

195.00 

K 

39-11 

Se 

79.00 

28.40 
107.90 

23-05 
87.60 


5 

32.06 

Te 

125.00 

Sn 

119.00 

Zn 

65-30 

j  I 

(  VII 

II 

IV 

II 

IV 

II 
II 

VII 

I 
II 

i  II 

(VIII 

V 

i  II 

\    VI 

V 

II 

IV 

I 

j  II 

I    VI 
IV 

I 
I 
II 

i  II 

(    VI 

II 
II 

IV 

II 


125.85 
17.98 

28.00 
14.00 

103.48 

51-74 

12.15 

27.50 

7.86 

200.00 

100.00 

29.00 

7-25 
2.81 
8.00 
2.67 
6. 20 

97-50 
48.75 

39-11 
39-50 

13-17 

7. 10 

107.90 

23-05 
43.80 
16.03 

5-34 
62.50 

59-50 

29-75 
32-65 


.00130300 
.00018630 
.00029010 
.00014500 
.00107200 
.00053600 
.00012590 
.00028490 
.00008143 
.00207200 
.00103600 
.00030040 
.00007510 
.00002911 
.00008288 
.00002766 
.00006423 
.00101000 
.00050500 
.00040520 
.00040920 
.00013640 
.00007355 
.001 1 1800 
.00023880 
-00045370 
.00016610 
.00005532 
.00064750 
.00061640 
.00030820 
.00033820 


The  names  of  the  non-metallic  elements  are  printed  in  italics. 


1694  BATTERIES. 

2562.  In  indicating  the  elements  wiiich  make  up  any 
substance,  the  symbols  of  those  elements  are  commonly  used ; 
also,  to  indicate  the  number  of  atoms  (if  more  than  one)  in 
the  molecule,  a  small  number  is  suffixed  to  the  symbol.  The 
expression  of  the  chemical  constitution  of  a  substance  by 
means  of  the  symbols,  with  the  relative  number  of  atoms  of 
each  element  suffixed,  is  called  the  chemical  formula  of 
that  substance. 

Thus,  a  substance  (water)  whose  formula  is  H/J  is  com- 
posed of  hydrogen  and  oxygen,  and  each  molecule  of  water 
is  composed  of  two  atoms  of  hydrogen  and  one  of  oxygen. 
The  atomic  weights  of  H  and  O  (from  Table  89)  are  1  and 
16,  respectively.  Therefore,  any  weight  of  water  is  com- 
posed of  2  X  1  =  2  parts  by  weight  of  hydrogen  and  16X1  = 
16  parts  by  weight  of  oxygen.  It  follows,  then,  that  the 
weight  of  1  molecule  of  water  will  be  2  +  IG  =  18  ;  if  1  gram 
of  water  were  decomposed  there  would  result  -^-^  =  .1111  + 
gram  of  hydrogen  and  ||  =  .8889—  gram  of  oxygen. 
(Compare  this  with  Art.  2493.) 

2563.  An  apparent  exception  to  the  above  statements 
is  the  metal  mercury,  which  seems  to  unite  with  most  of  the 
other  metals  in  all  proportions,  forming  amalgams  of  the 
metals.  These  amalgams,  however,  are  generally  considered 
to  be  merely  mechanical  mixtures,  and  not  true  chemical 
compounds.  Some  metals,  such  as  zinc,  gold,  silver,  lead, 
and  others,  form  amalgams  at  ordinary  temperatures,  it  be- 
ing merely  necessary  to  clean  the  surface  of  the  metal  thor- 
oughly before  placing  it  in  contact  with  the  mercury. 

An  amalgamated  metal  in  a  chemical  formula  is  indicated 
by  placing  the  symbol  Hg  after  and  above  the  symbol  of  the 
metal  amalgamated;  thus,  Zn^^' 

2564.  As  the  same  elements  occur  in  many  different 
substances,  it  is  evident  that  they  must  be  capable  of  repla- 
cing each  other;  that  is,  in  a  molecule  of  a  given  substance 
the  atoms  of  one  element  present  can  be  replaced  by  a  certain 
number  of  atoms  of  another,  thus  forming  a  new  compound. 
This  number  is  not  necessarily  the  same  as  the  number  of 


BATTERIES.  1695 

atoms  of  the  element  replaced.  For  example,  one  atom  of 
carbon  [C)  can  replace  \.\i&  four  atoms  of  hydrogen  (//)  con- 
tained in  two  molecules  of  water  {'iH^O),  forming  CO^. 
From  this  it  follows  that  the  zveight  of  one  clement  which  zviU 
replace  nnit  %veig]it  of  another  element  in  a  compound  is  not 
always  the  same  as  the  ratio  of  the  atomic  weights  of  the  tivo 
elements.  The  weight  of  the  replacing  element  may  be  said 
to  be  the  (chemical)  equivalent  of  unit  weight  of  the  replaced 
element.  Taking  for  the  standard  replaced  element  the 
lightest,  hydrogen,  and  calling  its  unit  weight  1,  the  least 
weight  of  any  other  element  which  will  replace  1  part  by 
weight  of  hydrogen  in  a  compound,  or  will  unite  with  1  part 
by  weight  of  hydrogen,  is  its  actual  chemical  &i\\x^^&.- 
l^w^ty  or  combining  zveight.  (See  column  5,  Table  89.)  The 
chemical  equivalent  of  hydrogen  is  evidently  the  same  as  its 
atomic  weight,  1.  Now,  in  binary  compounds  (compounds 
consisting  of  only  two  elements)  containing  hydrogen,  the 
proportion  of  the  hydrogen  in  the  compound  is  never  less 
than  1  atom  of  7/ to  1  atom  of  the  other  element,  though 
often  more;  consequently,  from  the  definition,  the  chemical 
equivalent  is  never  greater  than  the  atomic  weight,  and  may 
be  less. 

2565.  The  ratio  of  the  atomic  weight  to  the  chemical 
equivalent  of  an  element  is  thus  equal  to  or  greater  than  1. 
In  fact,  as  it  is  considered  that  there  are  comparatively  few 
atoms  of  each  element  in  any  molecule,  this  ratio  is  always 
small,  and  always  a  whole  number.  This  ratio  is  also  the 
number  of  atoms  of  hydrogen  which  would  be  required  to  re- 
place one  atom  of  the  given  element,  and  is  called  the  va- 
lency, or  atomicity,  of  the  element.  The  valency  of  the 
more  common  elements  is  given  in  column  4,  Table  89.  It 
can  also  be  shown  from  the  above  statements  that  the  number 
of  atoms  of  one  element  required  to  replace  a  given  number 
of  atoms  of  another  element  which  are  in  combination  with 
a  given  number  of  atoms  of  a  third  element  is  inversely  pro- 
portional  to  the  respective  valencies  of  the  replaced  and  re- 
placing elements. 


1696  BATTERIES. 

For  example,  each  molecule  of  water  {H^O)  contains  two 
atoms  of  //and  one  of  O.  If  the  (9,  whose  valency  is  II,  is 
replaced  by  CI,  whose  valency  is  I,  each  of  the  two  atoms  of 
H  will  combine  with  one  atom  of  CI,  forming,  not  H^Cl^^ 
but  two  molecules  of  HCl  (written  ^HCl).  Thus,  two 
atoms  of  CI  of  valency  I  are  required  to  replace  one  atom 
of  oxygen  of  valency  II, 

2566.  Elements  sometimes  combine  in  other  propor- 
tions than  the  above  statements  would  allow;  but  such  sub- 
stances are  seldom  stable,  readily  uniting  with  additional 
atoms  of  the  proper  elements  until  the  proportions  are  as 
indicated  by  the  valencies.  However,  some  elements  seem 
to  have  two  different  valencies,  as  will  be  noticed  in  column 
4,  Table  89;  the  lower  valencies  give  the  more  stable  com- 
pounds. It  should  be  remembered  that  the  above  principles 
of  atomic  weight,  valency,  etc.,  are  not  the  expression  of 
any  chemical  theory,  but  the  result  of  long  and  careful  ob- 
servation and  measurement;  this,  however,  is  not  infallible, 
and  apparent  violations  of  the  foregoing,  statements  will  be 
encountered,  though  they  may  be  generally  used  with  con- 
sistent results. 

2567.  At  ordinary  temperatures  and  pressures,  five  of 
the  elements,  hydrogen,  oxygen,  nitrogen,  fluorine,  and 
chlorine,  are  gases;  mercury  and  bromine  are  liquids;  while 
all  the  rest,  including  all  metals  excepting  mercury,  are 
solids.  All  the  solids  except  carbon  have  been  liquefied  at 
various  temperatures. 

Few  elements,  except  the  more  common  metals  and  oxy- 
gen and  nitrogen,  are  extensively  used  or  found  in  an  un- 
combined  state;  they  usually  occur  in  various  combinations,, 
which  are  divided  into  three  classes:  acids,  bases,  and  salts. 

2568.  An  acid  may  be  defined  as  a  compound  con- 
taining hydrogen,  which  hydrogen  may  be  replaced  by  a 
metal  when  presented  to  it  in  the  form  of  an  oxide  or  hy- 
drate. The  combination  of  oxygen  with  any  other  single 
element  is  called  an  oxide.     A  hydrate  is  the  substance 


BATTERIES. 


1697 


formed  by  the  union  of  an  element,  or,  more  often,  a  me- 
tallic oxide,  with  the  elements  of  water.  This  should  not 
be  confounded  with  a  solution,  which  is  merely  a  mechan- 
ical mixture  of  some  solid  with  water,  or  similar  liquid. 

Acids  are  usually  sour  to  the  taste,  and  will  readily  cause 
chemical  action.  Most  acids  contain  oxygen,  being  formed 
from  the  union  of  an  oxide  of  a  non-metal  and  water;  but 
in  some  few  acids  oxygen  is  absent.  Table  90  gives  a  list 
of  the  more  common  acids,  with  their  chemical  formulas 
and  other  data. 

TABLE   90. 

COMMON   ACIDS. 


r. 

Name  of  Acid. 

3. 
Chemical 
Formula. 

r. 

Specific  Gravity. 

3. 
Pure  Acid. 

4. 

Commercial  Acid. 

(Average.) 

Hydrochloric 

Hydrobromic 

Nitric 

HCl 
HBr 

HNO^ 

H^CrO, 

1.227 
1.515 
1.530 
1.846 

1.14  to  1.16 

1.33  to  1.41 

Sulphuric 

1.70  to  1.83 

Chromic     

Note. — HCl  and  HBr  are  in  reality  gases,  which  dissolve  readilj- 
in  water,  forming  the  liquid  known  by  the  above  names.  The  specific 
gravity  given  is  that  of  the  solution  (maximum). 

2569.  A  base  is  a  compound,  usually  an  oxide  or 
hydrate,  of  a  metal,  which  metal  is  capable  of  replacing  the 
hydrogen  of  an  acid  when  the  two  are  in  contact.  Some 
particularly  active  bases  are  known  as  alkalies^  which  are 
soluble  in  water.  The  principal  alkalies  are  sodium  hydrate, 
NaOH,  potassium  hydrate,  KOH,  and  ammonium  hy- 
drate (aqua  ammonia),  NH jOH. 

2570.  A  salt  is  the  substance  resulting  from  the  re- 
placement of  the  hydrogen  of  an  acid  by  the  metal  of  a  base, 
The  action  of  the  stronger  acids  and  bases  on  each  other  is 


1698  BATTERIES. 

very  violent.     By  some  chemists  the  acids  are  considered  to 
be  salts  of  hydrogen. 

Some  combinations  of  non-metallic  elements  act  in  many 
ways  similar  to  the  metals,  and  can  form  oxides  and  hydrates 
and  bases,  and  replace  the  hydrogen  in  acids,  and  tnese 
groups  of  elements  should  be  included  in  the  above  denni- 
tions.  Such  a  group  is  NH^^  which  is  sometimes  called 
amnionium.  There  are  several  other  similar  groups. 
They  act  and  may  be  handled  as  elements;  their  valency  is 
the  difference  between  the  valency  of  the  separate  elements. 
Thus,  in  the  above  case,  NH^^  the  valency  of  N  is  V,  while 
that  of  77,  is  4  X  I  =  IV;  hence,  the  valency  of  NH^  — 
V  -  IV  =  I. 

2571.  In  chemistry,  substances  are  given  names  in 
accordance  with  their  composition,  although  many  of  the 
more  common  substances  have  popular  names.  For  ex- 
ample, the  crystals  of  copper  sulphate  are  popularly  known 
as  blue  vitriol.  Ordinary  compounds  of  a  metal  and  non- 
metal  are  named  from  both  components.  The  Latin  name 
of  the  metal  is  given  first,  and  for  its  last  syllable,  uni,  is 
substituted  ic\  to  this  is  added  the  name  of  the  non-metal, 
with  its  last  syllable  changed  to  ide.  Thus,  a  compound  of 
iron  and  sulphur  is  named  y^rrzV  sulphide. 

In  the  case  where  an  element  has  two  valencies,  distinc- 
tion is  made  between  the  two  compounds  which  may  be 
formed  from  the  same  elements  by  substituting  the  termi- 
nation oiis  for  ic  in  the  name  of  the  metal,  when  referring  to 
the  compound  having  the  lower  proportion  of  the  non- 
metallic  element,  which  is  usually  oxygen.  For  example, 
copper  forms  two  oxides:  ciipric  oxide,  CtiO,  and  enprous 
oxide,  Cu^O.  The  prefixes  per  and  proto  are  sometime3 
used  instead  of  the  terminations  ic  and  07is,  respectively. 
The  names  of  acids  are  derived  from  their  principal  constit- 
uent (aside  from  the  hydrogen)  by  changing  the  last  sylla- 
bles of  its  name  to  ic.  Thus,  the  principal  acid  formed  from 
sulphur  is  called  stilphuric  acid  {H^SO^.  The  acids  which 
do  not  contain  oxygen  are  distinguished  by  the  prefix  hydro^ 
as  hydrobromic  acid  {HBr.\     (See  Table  90.) 


BATTERIES.  1699 

2572.  The  names  of  the  salts  resulting  from  the  action 
between  bases  and  acids  are  derived  from  the  name  of  the 
acid  by  taking  the  first  syllable  of  the  principal  constituent 
of  the  acid  and  adding  ate.  Thus,  salts  formed  from  bases 
and  sulphuric  acid  are  named  sulphates,  and  from  nitric 
acid,  nitrates. 

In  the  case  where  oxides  are  formed  with  non-metals  of 
more  than  one  valency,  the  acids  formed  from  such  oxides 
by  their  union  with  water  take  the  ic  and  oils  terminations, 
just  as  the  metallic  compounds  do.  For  example,  there  are 
two  oxides  of  sulphur,  SO^  and  SO^.  The  acid  formed 
from  the  first  is  known  as  sulphurous  acid,  and  from  the 
second  sulpJiiiric  acid.  The  salts  of  an  acid  ending  in  ic 
have  the  termination  ate,  .as  stated  above,  while  the  salts 
of  the  Otis  acids  end  in  ite.  It  is  evident,  from  the  use  of  the 
terminations,  that  the  ate  salts  and  the  ic  oxides  contain 
greater  proportions  of  oxygen ;  ite  salts  and  ous  oxides  are 
usually  unstable,  readily  combining  with  oxygen  to  form 
the  higher  salts  or  oxides. 


ELECTROCHEMISTRY. 

2573.  A  current  of  electricity  passing  through  a  con- 
ducting liquid  will  decompose  the  liquid,  the  amount  of  the 
various  elements  set  free  being  proportional  to  the  quantity 
of  electricity  passing  through  the  liquid.      (Art.  2493.) 

The  amount  (weight)  of  any  element  which  will  be  liber- 
ated by  a  given  quantity  of  electricity  X'S,  proportional  to  the 
cJiemical  equivalent  of  that  element ;  hence,  from  the  amount 
of  hydrogen  (or  other  element  whose  valency  is  always  I) 
set  free  by  unit  quantity  of  electricity,  the  amount  of  any 
other  element  that  will  be  set  free  by  the  same  quantity  of 
electricity  may  be  calculated.  The  chemical  equivalent  of 
hydrogen  being  1,  the  amount  of  hydrogen  liberated  by  one 
coulomb  of  electricity  becomes  a  multiplier,  and  by  multi- 
plying  the  chemical  equivalent  of  each  element  by  this  mul- 
tiplier the  electrochemical  equivalents,  or  the  weight 
of  each  element  liberated  per  coulomb,  results.  (See  col- 
umn 6,  Table  89.) 


1700  BATTERIES. 

2574,  There  is  reason  to  believe  that  all  chemical 
action  generates  E.  M.  F. ;  but  in  order  that  this  E.  M.  F. 
may  be  utilized,  the  chemical  action  must  take  place  in  and 
between  conducting  bodies. 

In  order  that  the  E.  M.  F.  may  be  continuously  main- 
tained— that  is,  that  the  chemical  action  be  continuous 
— at  least  one  of  the  bodies  acted  upon  must  be  a  liquid. 
This  liquid  is  called  the  electrolyte  (see  Art.  2238).  An 
electrolyte  does  not  necessarily  contain  water;  it  may  even 
be  made  by  melting  one  of  the  elements  of  the  cell. 

2575.  The  simplest  form  of  a  cell  consists  of  at  least 
two  bodies,  of  which  one  at  least  must  be  a  liquid,  in  and 
between  which  two  bodies  the  chemical  action  goes  on  which 
generates  the  E.  M.  F.  In  order  that  this  E.  M.  F.  may  be 
utilized  to  cause  a  current  to  flow,  provision  must  be  made 
for  connecting  an  external  circuit  with  the  two  bodies 
between  which  the  action  takes  place. 

Such  a  cell  is  usually  composed  of  an  electrolyte  (often 
called  the  exciting  liquid),  into  which  are  placed  two  con- 
ducting bodies;  at  least  one  of  the  bodies  is  metallic,  and  it 
is  between  this  body,  called  the  anode,  and  the  electrolyte 
that  the  chemical  action  takes  place. 

Strictly  speaking,  the  surface  of  contact  between  the 
liquid  and  the  metal  is  the  place  of  action,  and  would  more 
properly  be  called  the  anode. 

The  other  body,  called  the  cathode,  serves  mainly  as  a 
means  of  connecting  the  external  circuit  to  the  electrolyte, 
the  other  end  of  the  circuit  being  connected  to  the  anode. 
Connection  is  actually  made  to  the  parts  of  the  anode  and 
cathode  which  project  from  the  cell,  these  being  then  called 
the  electrodes  of  the  cell.  This  is  the  usual  construction, 
although  in  some  cells  the  chemical  action  takes  place  be- 
tween two  different  liquids,  in  which  case  whatever  solid 
conducting  bodies  are  used  act  merely  as  connectors  or 
terminals. 

Examples  of  such  cells  will  be  pointed  out  in  the  descrip- 
tion of  the  various  types. 


BATTERIES.  1701 

2576»  The  chemical  action  which  takes  place  is  as  fol- 
lows :  When  the  two  elements  of  the  cell  are  placed  in  the 
electrolyte,  the  fact  of  there  being  2i  chemical  affinity  het^QQn 
the  various  substances  in  the  cell  sets  up  a  difference  of 
potential,  which  appears  as  between  the  terminals  of  the 
cell;  this  affinity  may  or  may  not  set  up  a  chemical  action, 
but  so  long  as  the  external  circuit  is  open,  whatever  action 
may  occur  is  only  local,  and  its  energy  appears  as  heat. 
The  reason  that  no  chemical  action  occurs  is  that  the  atoms, 
having  combined,  have  given  up  most  of  their  potential 
energy,  and  so  remain  in  the  combinations  they  have  as- 
sumed; as  soon,  however,  as  the  external  circuit  is  closed, 
the  difference  of  potential  which  exists  equalizes  itself,  and 
causes  a  momentary  current  to  flow  through  the  external 
circuit  yr^7;2  the  cathode  to  the  anode,  the  cathode  being  at 
the  higher  potential. 

This  current  decomposes  the  electrolyte,  breaking  up  the 
compounds  therein  and  restoring  to  the  various  atoms  their 
potential  energy.  Some  of  these  atoms  then  unite  with  the 
material  of  the  anode,  and  the  E.  M.  F.  is  maintained, 
causing  the  flow  of  current  to  be  continuous. 


ELECTROCHEMICAL    CALCULATIONS. 

2577.  In  the  following  we  shall  show  the  exact  relation 
existing  between  the  current  and  the  chemical  work;  that 
is  to  say,  we  shall  show  how  to  calculate  the  amount  of 
chemical  work  which  a  given  current  can  perform,  and,  con- 
versely, the  quantity  of  current  evolved  when  a  definite 
amount  of  chemical  work  is  done. 

2578.  Whenever  an  electrolyte  is  decomposed  by  a 
current,  the  resolved  elements  have  a  tendency  to  reunite. 
This  tendency  is  termed  chemical  affinity.  Thus,  when 
an  electric  current  has  been  sent  through  a  solution  of  zinc 
sulphate  {ZnSO^),  and  the  solution  has  thereby  been  split 
up  into  zinc,  oxygen,  and  sulphur,  then,  as  soon  as  the 
current  ceases  to  flow,  the  zinc  exhibits  a  tendency  to 
recombine  chemically  with  the  disintegrated  solution.     This 


1703  BATTERIES. 

tendency  represents  the  strong  chemical  affinity  of  zinc  for 
oxygen  and  sulphur.  Also,  when  acidulated  water  has  been 
decomposed  electrically,  the  separated  oxygen  and  hydrogen 
tend  to  reunite. 

2579.  This  tendency  to  reunite  is  strikingly  shown  by 
an  electromotive  force  which  is  set  up  in  the  solution  after 
the  decomposing  current  ceases.  This  E.  M.  F.  can  be 
shown  to  exist  by  connecting  a  galvanometer  in  circuit  with 
the  decomposed  solution.  The  deflection  of  this  instrument 
will  show  that  this  E.  M.  F.  due  to  chemical  affinity  acts 
in  the  opposite  direction  to  the  E.  M.  F.  of  the  decomposing 
current.     In  other  words,  it  is  an  opposing  electromotive  force. 

2580.  Careful  measurement  has  shown  that  when 
hydrogen  and  oxygen  combine  with  each  other,  an  electro- 
motive force  of  1.47  volts  is  set  up.  From  this  it  follows 
that  no  water  can  be  decomposed  unless  an  electromotive 
force  of  at  least  1.47  volts  is  utilized;  for  it  requires  this 
much  alone  to  offset  the  opposing  E.  M.  F.  of  recombination. 

2581.  With  every  electrolyte  there  is  a  similar- mini- 
mum E.  M.  F.  necessary  to  produce  continuous  decomposi- 
tion. This  E.  M.  F.  can  be  calculated  for  any  electrolyte  if 
the  heat  of  formation  and  the  electro-chemical  equivalent  of 
its  constituents  are  known.  The  heat  of  formation  is  the 
thermocliemical  equivalent  of  the  substance.  By  the 
thermochemical  equivalent  is  meant  the  amount  of  heat 
liberated  by  the  chemical  combination  of  the  molecular 
weight  of  one  substance  with  another.  This  energy  is 
usually  expressed  in  gram-calories;  that  is,  the  amount  of 
heat  necessary  to  raise  the  temperature  of  one  gram  of 
water  1°  Centigrade.  This  thermochemical  equivalent  is 
a  value  found  by  careful  experiment.  Thus,  one  gram  of 
zinc,  for  instance,  converted  into  zinc  sulphate  (ZnSO ^,  is 
known  by  experiment  to  give  off  about  4,000  heat-units  as 
it  combines.  In  Table  91  the  heat  of  formation  of  various 
substances  with  oxygen  is  given. 


BATTERIES. 


1703 


TABLE  91. 

HEAT   OF   COMBINATIOIV   WITH    OXYGEN. 


1  Gram  of 


Hydrogen  . 
Carbon. . . . 
Sulphur.  .  , 
Phosphorus 
Zinc. ..... 

Iron 

Tin 

Copper  . . . 


Calories  or  Gram 

Degrees  of  Heat 

Produced. 

34,000 
8,000 
2,300 
5,747 
1,301 
1,576 
1,233 
602 


2582.  Electrochemical  Equivalent. — Experiment 
has  shown  that  when  1  C.  G.  S.  iinit  of  current  (Art. 
2268)  passes  through  water,  it  liberates  .0001036  gram  of 
hydrogen.  Now,  since  1  C.  G.  S.  unit  of  current  equals  10 
practical  units  or  coulombs  (Art.  2278),  it  is  evident  that 
1  coulomb  will  liberate  only  J^  of  this  weight  of  hydrogen, 
or  1  coulomb  liberates  .00001036  gram  of  hydrogen.  This 
quantity  of  hydrogen  is  always  liberated  by  1  coulomb  of 
current,  and  similarly  1  coulomb  of  current  will  liberate  a 
certain  definite  weight  of  any  other  electrolytic  substance. 
The  weight  thus  liberated  by  1  coulomb,  or  by  1  ampere 
flowing  for  1  second,  is  termed  the  electrocUemical 
equivalent  of  the  substance,  and  may  be  found  tabulated 
for  the  most  important  elements  in  column  6  of  Table  89. 

2583.  Total  l?^eight  Liberated  by  Chemical 
Action. — Experiment  has  furthermore  shown  that  the  total 
weight  of  any  substance  liberated  by  chemical  action  is 
directly  proportional  to  the  quantity  of  current  flowing,  so 
that  if 

z  =  electrochemical  equivalent  of  any  substance; 

Q  ■=■  number  of  coulombs; 

W  =^  weight  in  grams  of  liberated  substance; 

then,  W==Q^z.  (467.) 


1704  BATTERIES. 

Example. — A  current  of  .5  ampere  was  passed  through  an  acidulated 
solution  of  water  for  10  minutes.  "What  weight  of  hydrogen  was 
evolved  ? 

Solution. —  /  =  10  minutes  =  600  seconds.  (7=. 5  ampere.  Then, 
by  formula  405,  Q  =  C/  =  .5  X  600  =  300  coulombs.  Referring  to 
column  6,  Table  89,  we  find  for  hydrogen  ^^  =  .00001036;  hence,  by 
formula  467,  IV=  300  X  .00001036  =  .003108  gram  of  hydrogen.    Ans. 

2584.  Heat    Formation    by   Chemical    Action. — 

In  Art.  2581  the  formation  of  heat  during  chemical 
action  was  explained.  Experiment  has  shown  that  the  total 
heat  generated  during  chemical  action  is  proportional  to  the 
weight  of  the  substance  liberated;  so  that  if 

/i  =  calories  evolved  per  gram  of  substance; 

IV  =  weight  in  grams  of  substance  liberated; 

U  =  total  calories  evolved ; 

then,  -  H—  Wx  h\ 

but,  inserting  the  value  of  W  as  given  by  formula  467,  we 
have  as  the  total  heat  evolved  in  calories 

H^Qxzxh.  (468.) 

2585.  Relation    of  Heat   and    V^ork. — It    can    be 

shown  by  a  simple  calculation,  knowing  the  inechanical 
equivalent  of  heat,  that  1  calorie  is  equivalent  to  4.2  joules 
of  work.  This  being  the  case,  formula  468  may  be  written 
to  express  the  total  joules  ^  of  energy  required  to  liberate  a 
given  weight  of  any  substance;  for,  if  y^=:  total  joules  of 
energy,  then,  by  utilizing  the  notation  of  Art,  2584, 

/=4.2  Qx^Xh.  (469.) 

2586.  It  is  possible  to  express  this  work  in  another 
manner.  By  referring  to  Art.  2332,  it  will  be  seen  that 
the  work  done  in  joules  in  any  electrical  circuit  can  be 
expressed  by  the  product  of  volts  and  coulombs  of  that  cir- 
cuit; or,  if 

E  =  volts; 

Q  =  coulombs ; 

/  =  joules; 

then,  J^ExQ.  (470-) 


BATTERIES.  1705 

2587.  Calculation  of  E.  M.  F.  Produced  by 
Chemical  Action. — Comparing  formulas  469  and  470, 
we  see  that  they  are  different  expressions  for  the  same 
quantity  y,  namely,  the  electrical  work  in  joules  done  in  the 

circuit;  or, 

/  =  4. 2  Qyis  X  h^  and 

'j=ExQ. 

But,  when  two  quantities  are  each  equal  to  a  third,  they 
are  equal  to  each  other;  hence, 

^X  0  =  4.2  0  X^X/^. 

Dividing  both  sides  of  this  equation  by  Q  gives  us  an  ex- 
pression for  the  electromotive  force  in  volts,  namely, 

^^4.2/^X^.  (471.) 

This  important  result  may  be  expressed  in  words  as 
follows:  The  electrovwtive  force  in  volts  of  any  chewical 
reaction  is  equal  to  the  product  of  the  electrochemical  equiva- 
lent of  the  separated  substance,  the  heat  of  combination  of  the 
substance  per  gram  degree,  and  tlie  constant  Ji..2. 

Example. — Calculate  the  opposing  E.  M.  F.  set  up  by  the  hydrogen 
tending  to  unite  with  the  oxygen  during  the  decomposition  of  water. 

Solution. — Refer  to  Table  89,  column  6,  where  for  hydrogen  2  = 
,00001036,  and  to  Table  91,  column  3,  where  for  hydrogen  /z  =  34,000; 
then,  by  formula  471 ,  £  =  4.2  X  34,000  X  .00001036  =  1.479  volts.    Ans. 

Note. — In  the  same  way  we  may  calculate  the  opposing  E.  M,  F.  set 
up  and  effecting  any  particular  electrolysis. 

2588.  In  the  above,  the  E.  M.  F.  is  calculated  on  the 
assumption  that  all  the  chemical  energy  developed  is  con- 
verted into  electricity,  and  that  none  of  the  energy  appears 
as  heat.  Practically,  however,  some  heat  is  generated  in 
almost  every  case  during  the  electric  activity.  This  is  only 
a  secondary  consequence  of  the  electric  resistance  of  the 
cell.  If  the  cell  offers  a  negligible  resistance,  then  the 
amount  of  heat  electrically  developed  by  the  current  would 
also  be  negligible,  and  all  the  chemical  energy  developed  by 
chemical  changes  in  the  cell  would  be  liberated  outside  the 
cell,  that  is,  in  the  external  circuit. 


1706  BATTERIES. 

2589.  It  should  be  remarked,  however,  that  owing 
to  the  incompleteness  of  our  knowledge  of  thermo- 
chemical  equivalents,  and  of  the  exact  nature  of  the  electro- 
chemical actions  in  the  cell,  the  E.  M.  F.  of  a  cell  can  only 
in  a  few  instances  be  practically  predetermined. 


ELECTROCHEMICAL    THEORIES. 

2590.  If  more  than  one  set  of  actions  can  take  place 
in  a  cell,  the  effect  of  the  various  actions  on  the  E.  M.  F.  of 
the  cell  may  be  determined  by  properly  applying  formula 
471  to  each  action;  the  E.  M.  F.  of  each  action  may  be 
then  added  or  subtracted  to  get  the  resulting  E.  M.  F., 
according  to  the  nature  of  the  action. 

If  the  substance  forming  the  anode  has  an  affinity  for  one 
or  more  elements  of  the  electrolyte,  and  the  substance  form- 
ing the  cathode  has  an  affinity  for  the  other  element  or  ele- 
ments of  the  electrolyte,  it  is  evident  that  the  tendencies  of 
these  elements  to  combine  with  the  anode  and  cathode,  re- 
spectively, will  assist  each  other,  and  the  E.  M.  F.  of  each 
action  will  add  together  in  giving  the  resulting  E.  M.  F.  of 
the  cell. 

If  the  substances  forming  the  anode  and  cathode,  respect- 
ively, have  each  an  affinity  for  tJic  same  element  or 
elements  of  the  electrolyte,  it  is  again  evident  that  the 
tendency  of  these  elements  to  combine  with  the  anode  will 
be  partly  balanced  by  their  tendency  to  combine  with  the 
cathode;  hence,  the  E.  M.  F.  which  would  result  from 
either  action  alone  must  be  subtracted  from  the  other  to 
obtain  the  resulting  E.  M.  F. 

This  explains  the  case  spoken  of  in  Art.  2243,  where  it 
is  stated  that  a  cell  with  zinc  and  iron  as  elements  will  give 
a  less  E.  M.  F.  than  a  cell  using  zinc  and  graphite  (carbon). 
In  the  zinc-iron  cell  a  part  of  the  electrolyte  has  an  affinity 
for  both  the  zinc  and  the  iron,  while  in  the  zinc-graphite 
cell  the  electrolyte  has  no  affinity  for  the  graphite,  and  the 
full  E.  M.  F.  of  the  action  on  the  zinc  appears.  The  mean- 
ing of  the  Electromotive  Series  (Art.  2241)  should  now 
be  clear,  .  > 


BATTERIES.  1707 

2591.  The  action  which  takes  place  in  a  cell  if  the 
electrolyte  be  an  acid  is  the  decomposition  of  the  acid,  the 
liberation  of  the  hydrogen,  and  the  formation  of  a  salt  of  the 
metal  of  the  anode  by  its  union  with  the  balance  of  the  acid. 
If  the  electrolyte  be  a  solution  of  some  salt,  the  action  is 
more  complicated,  and  is  about  as  follows  :  The  water  of 
the  solution  is  decomposed,  its  oxygen  uniting  with  the 
anode,  forming  an  oxide,  and  the  hydrogen  is  liberated,  as 
before.  The  oxide  which  is  formed  then  unites  with  the 
salt  in  solution,  forming  salts  of  the  metal  oxidized;  these 
formations  increase  the  E.  M.  F.  which  the  cell  would  have 
were  water  alone  the  exciting  liquid  and  the  oxidation  of  the 
anode  the  only  action. 

2592.  Thus  it  is  seen  that  in  almost  all  the  chemical 
actions  which  occur  in  batteries,  the  attacking  of  the  anode 
results  from  the  decomposition  of  the  electrolyte,  hydrogen 
being  liberated.  This  decomposition  of  the  electrolyte 
takes  place  throughout  the  space  between  the  anode  and 
cathode;  the  hydrogen,  however,  does  not  appear  through- 
out the  electrolyte,  but  only  at  the  surface  of  the  cathode; 
for  as  soon  as  the  electrolyte  is  decomposed  into  its 
elements,  the  union  of  the  metal  of  the  anode  with  the  ele- 
ments of  the  electrolyte  with  which  it  can  combine  can  only 
take  place  with  the  atoms  of  the  particular  molecules  which 
were  at  the  surface  of  the  anode;  the  free  hydrogen  atoms 
of  these  molecules  then  unite  with  the  free  elements  of 
what  was  the  next  layer  of  molecules,  reforming  the  original 
electrolyte;  the  displaced  hydrogen  atoms  of  these  newly 
formed  molecules  unite  with  the  free  elements  of  the  next 
layer  of  molecules,  and  so  on  all  across  the  liquid,  until  at 
the  point  where  the  current  leaves  the  liquid  (the  cathode) 
there  are  left  the  free  hydrogen  atoms  of  the  last  layer  of 
molecules.  These  then  appear  at  the  surface  of  the  cathode, 
providing  the  cathode  is  not  a  substance  with  which  these 
free  atoms  may  unite. 

2593.  The  accompanying  diagrams  represent  this  ac- 
tion in  the  case  of  the  zinc   {Zn),  sulphuric  acid   {H^SO^), 


1708 


BATTERIES. 


and  copper  {Cu)  cell,  given  in  Art.  2240.  One  single  line 
of  the  molecules  of  the  electrolyte  between  the  zinc  and 
the  copper  plate  is  represented  at  a,  Fig.  1037.  Each 
molecule  of  the  acid  is  made  up  of  one  atom  of  vS  and  four 
of  O,  united  with  a  molecule  consisting  of  two  atoms  of  H. 


in 


[5o:ni?i?  i[i^i?  I?  i[io:]i-?  i?  iiisnlTTTliaonRnTl 


(io3  H  H  [^  [Z]  [zi  [1^  m  [iDii^m  [Z]  [^m  cz 


[^  [ff]  [^  m  [Zl  [^  m  m  [^  S  E  [^  m  [Z]  (^ 


\SOt  \  H  \  B~\  \SOt  I  g  I  H~\  I  aOt\   B  I  H~l  \SOt\  B  |  H~\  1 50«|  B  |  B^ 


I  g  I  l-g   I  \SO,\  H   I  hH  liSQ^I  -g  I  -H~l  ISQ^I  B  \  B~\  |.SQ^|  g    |  B~\  [go7 


Fig.  1037. 

No  current  is  supposed  to  be  flowing  through  the  liquid. 
For  convenience,  it  is  assumed  that  the  molecule  of  S0^  is 
not  decomposed  by  the  current;  actually,  it  probably  is,  but 
since  in  its  action  with  the  zinc  it  unites  with  it  as  a  whole, 
the  assumption  is  allowable. 

In  d,  Fig.  1037,  the  molecules  are  represented  as  decom- 
posed by  a  current,  and  each  individual  molecule  of  SO^ 
and  atom  of  H  is  separate.  Now,  the  molecule  of  SO^  at 
the  right  has  a  greater  affinity  for,  or  tendency  to  combine 
with,  the  zinc  than  it  has  to  combine  with  the  free  atoms  of 
//',  and  does  so,  as  represented  at  c,  Fig.  1037,  and  the  re- 
maining molecules  of  SO^,  not  being  in  contact  with  the 
zinc,  unite  with  the  free  atoms  of //^  all  the  way  across  the 
liquid,  until  at  the  copper  plate  there  are  no  free  molecules 
of  SO^  left  to  combine  with  the  last  atoms  of  //"in  the  line; 
consequently,  the  free  atoms  of  H  appear  in  the  form  of 


BATTERIES.  1709 

gas  at  the  copper  plate.  Of  course  the  newly  formed  mole- 
cules of  H^SO^  are  immediately  decomposed  and  reunited, 
which  process  continues  Avith  inconceivable  rapidity,  the 
result  being  a  practically  continuous  formation  of  ZnSO ^ 
at  the  anode  and  the  liberation  of  H  at  the  cathode  as  long 
as  any  current  flows  through  the  electrolyte.  Now,  it  is 
evident  that  all  the  energy  required  to  decompose  all  but 
one  molecule  in  any  line  of  molecules  across  the  electrolyte 
is  immediately  given  up  by  the  reunion  of  the  free  atoms. 
For  this  reason  the  distance  between  the  anode  and  the  cath- 
ode, or  their  size,  does  not  affect  the  amoitnt  of  electrolyte 
decomposed  by  a  given  force,  nor  the  energy  required  to  per- 
form the  decomposition. 


POLARIZATION    AND   DEPOLARIZATION. 

2594.  If  at  or  near  the  cathode  there  is  some  sub- 
stance, such  that  the  free  hydrogen  left  by  the  decomposi- 
tion of  the  electrolyte  may  unite  with  it,  the  energy  liberated 
by  such  formation  will  add  to  the  E.  M.  F.  of  the  cell.  If 
this  free  hydrogen  can  not  unite  with  some  substance  at  the 
cathode,  it  collects  on  the  surface  in  bubbles  as  a  gas.  In 
addition  to  the  reduction  of  the  E.  M.  F.  of  the  cell  due  to 
decomposition  of  the  electrolyte,  the  formation  of  hydrogen 
also  acts  disadvantageously,  as  it  forms  in  a  layer  on  the 
surface  of  the  cathode,  which  enormously  increases  the 
internal  resistance  of  the  cell,  thus  diminishing  the  current 
which  the  E.  M.  F.  of  the  cell  can  send  through  any  given 
external  resistance.  The  formation  of  hydrogen  on  the 
surface  of  the  cathode  is  known  as  polarization,  and  its 
removal,  by  any  means,  mechanical  or  chemical,  is  called  de- 
polarization, the  agent  used  being  called  the  depolarizer. 

2595.  If  merely  mechanical  means  of  depolarization 
be  used,  the  result  is  to  prevent  the  increase  of  internal 
resistance  of  the  cell;  by  causing  the  liberated  hydrogen  to 
recombine  at  the  cathode,  by  chemical  means,  not  only  is 
the  internal  resistance  not  increased,  but  the  actual  E.  M,  F. 
of  the  cell  is  increased. 


1710  BATTERIES. 

2596.  Various  mechanical  devices  for  depolarizing 
cells  have  been  used ;  the  cathode  has  been  arranged  to  be 
agitated  in  the  liquid,  or  to  be  entirely 'removed  from  the 
liquid  at  intervals;  or  the  cathode,  and  in  some  instances 
both  electrodes,  have  been  made  in  the  form  of  disks, 
dipped  for  about  half  their  diameter  into  the  electrolyte. 
On  rotating  the  disks,  the  hydrogen  is  prevented  from  form- 
ing on  the  cathode  by  its  motion. 

The  power  for  performing  these  various  movements  has 
usually  been  derived  from  clockwork,  and  in  some  instances 
from  the  current  given  out  by  the  battery.  It  is  evident 
that  such  devices  are  commercially  of  little  value,  especially 
as  chemical  depolarizers  may  be  easily  used. 

2597.  The  depolarization  by  chemical  means  may  be 
accomplished  by  surrounding  the  negative  element  (cathode) 
with  a  solid  or  liquid  substance,  with  which  the  free  hydro- 
gen may  combine.  This  combination  usually  merely  dis- 
poses of  this  element,  and  prevents  the  bad  effects  of  a 
deposit  on  the  cathode.  Under  these  circumstances  the 
compound  formed  at  the  cathode  is  usually  water,  the  de- 
polarizer being  a  substance  rich  in  oxygen,  with  which  the 
hydrogen  combines.  This  water  has  the  effect  of  diluting 
the  electrolyte,  already  weakened  by  the  combination  with 
the  anode;  but,  by  properly  selecting  the  depolarizer  with 
reference  to  the  electrolyte,  the  chemical  combination  at 
the  cathode  may  be  such  that  it  will,  either  directly  or  by 
further  combination,  replace  the  part  of  the  electrolyte 
which  has  combined  with  the  anode,  thus  keeping  the  elec- 
trolyte of  the  same  composition  and  strength  throughout 
the  life  of  the  anode  or  of  the  depolarizer.  Instances  of 
both  these  classes  of  chemical  depolarization  will  be  noted 
in  the  description  of  the  various  cells. 

2598.  The  rate  at  which  any  depolarizer  will  depolarize 
depends  on  many  conditions;  and  no  depolarizer  will  keep 
the  E.  M.  F.  of  a  cell  constant  for  all  currents,  for,  after  a 
certain  limiting  current  has  been  reached,  the  limit  depend- 
ing on  the  sizes  of  the  various  parts  of  the  cell,  the  formation 


BATTERIES.  1711 

of  the  free  element  of  the  electrolyte  is  more  rapid  than  its 
absorption  by,  or  recombination  with,  the  depolarizer,  and 
the  surplus  will  collect  on  the  cathode. 

In  the  case  of  depolarizers  which,  by  the  formation  of 
water,  dilute  the  electrolyte,  the  E.  M.  F.  will  become  less 
with  continued  use  of  the  cell,  even  if  the  current  output  be 
small.  These  facts  should  be  remembered  in  dealing  with 
the  various  depolarizers. 

2599.  From  the  preceding  remarks,  it  appears  that  in 
order  to  give  a  high  E.  M.  F.,  the  metal  chosen  for  the 
anode  must  be  one  whose  salts  have  a  comparatively  high 
value  for  their  heat  of  formation.  Such  metals  are  potassium, 
sodium,  strontium,  calcium,  and  magnesium;  potassium 
salts  having  the  highest  heat  of  formation,  the  others,  in  the 
order  given,  having  lower. 

2600.  Having  a  high  heat  of  formation  means,  however, 
that  the  metal  has  a  great  affinity  for  the  elements  necessary 
to  form  its  salts  or  oxides;  this  being  the  case,  they  are 
liable  to  combine  with  such  elements  whenever  the  opportu- 
nity presents  itself,  taking  them  from  the  air,  from  water,  or 
from  salts  of  other  metals  which  have  a  lesser  affinity  for  the 
salt-forming  elements.  Consequently,  the  metals  in  the  list 
given  could  not  be  used  in  the  presence  of  acids  or  solution 
of  salts,  or  even  of  water,  without  decomposing  the  liquid 
and  rapidly  forming  salts  or  oxides,  the  whole  of  the  energy 
of  the  action  appearing  as  heat.  In  order,  then,  to  have  a 
practicable  cell,  the  metal  should  not  be  attacked  by  the  ex- 
citing liquid  except  as  the  exciting  liquid  is  decomposed  by 
the  passage  of  the  current.  This  is  the  reason  for  the  ex- 
tensive adoption  of  zinc,  that  being  a  metal  whose  heat  of 
formation  is  comparatively  high,  at  the  same  time  not  high 
enough  to  cause  its  salts  and  oxides  to  be  formed  with  any 
degree  of  rapidity  unless  the  necessary  elements  are  pre- 
sented to  it  in  a  free  state,  as  they  are  in  a  voltaic  cell  by 
the  decomposition  of  the  electrolyte. 

Besides,  zinc  is  actually  the  cheapest  of  the  metals,  ex- 
cepting iron,  and,   in  proportion  to  the  amount  of  kinetic 


1712  BATTERIES. 

chemical  energy  possessed,  is  cheaper  than  any  other  metal 
which  could  be  used. 

2601.  Batteries,  as  sources  of  electrical  energy,  are 
used  mainly  in  cases  where  a  current  is  required  very  inter- 
mittently, such  as  in  ringing  bells,  lighting  gas,  etc.,  or 
where  a  small  but  steady  current  is  required  for  long  periods 
of  time,  as  in  telegraphy  and  telephony,  or  for  laboratory 
and  testing  purposes.  Their  general  use  on  a  large  scale,  as 
sources  of  electrical  energy  for  lighting  or  power  purposes, 
is  prohibited,  at  least  at  present,  by  the  comparatively  great 
cost  of  the  material  consumed,  and  the  expense  of  installa- 
tion and  maintenance. 

For  example,  the  bichromate  battery  is  about  the  cheapest 
in  point  of  cost  of  materials  consumed,  and  in  this  the  ma- 
terials alone  would  cost  about  28  cents  per  horsepower  per 
hour  on  a  large  scale,  while  the  cost  of  electrical  energy, 
using  dynamos,  is  about  5  or  6  cents  per  horsepower  per 
hour,  ordinarily,  and  in  many  cases  is  much  less.  The  cost 
of  material  in  the  silver  chloride  battery  is  about  $135  per 
horsepower  per  hour. 

This  high  cost  of  the  power  does  not,  however,  prevent 
batteries  from  being  largely  used  for  the  purposes  outlined 
above,  and  their  practical  application  is  an  important  part 
of  electrical  engineering. 


CELLS. 


CLASSIFICATION. 

2602.  The  various  classes  of  voltaic  cells  may  be 
divided  as  follows: 

Cells  in  ^iVhich  There  Is  No  Depolarizer. — This  is  the 
simplest  form  of  cell,  and,  on  account  of  polarization,  cells 
of  this  class,  commonly  called  open-circuit  cells,  are  not  used 
for  other  than  intermittent  work. 

2603.  Cells  TVitti  a  Depolarizing  Electrolyte. — In 

this  class  of  cells  the  electrolyte  is  of  such  a  nature  that 
either  no  hydrogen  is  formed  or  the  liquid  contains  a  sub- 


BATTERIES.  1713 

stance  with  which  the  hydrogen  unites.  As  this  action 
tates  place  mainly  at  the  cathode,  there  is  little  distinction, 
as  far  as  action  goes,  between  this  latter  type  and  cells  with 
a  liquid  depolarizer. 

2604.  Cells  W^ith  a  Liquid  Depolarizer. — In  this 
class  of  cells,  however,  the  cathode  is  surrounded  by  a  de- 
polarizing liquid,  which  is  prevented,  by  mechanical  means, 
from  mixing  with  the  electrolyte. 

The  means  usually  employed  are  either  to  separate  the 
two  liquids  by  a  porous  partition,  which  allows  of  their  elec- 
trical contact  without  mechanical  mixture  of  the  two,  if 
their  respective  specific  gravities  be  nearly  the  same ;  or,  if 
these  differ  considerably,  gravity  will  keep  the  two  liquids 
apart,  one  over  the  other  in  the  containing  vessel. 

2605.  Cells  With  a  Solid  Depolarizer. — This  class 
is  identical  in  action  with  the  class  preceding,  the  depolarizer, 
however,  being  a  solid  instead  of  a  liquid. 

If  the  solid  depolarizer  is  granular,  or  in  the  form  of  pow- 
der, it  is  often  necessary  to  employ  a  porous  partition 
between  the  cathode  surrounded  by  the  depolarizer  and  the 
electrolyte.  This  is  merely  to  keep  the  depolarizer  in  place, 
and  is  dispensed  with  if  the  depolarizer  is  formed  into 
a  paste  or  solid  body  upon  the  cathode.  In  fact,  the  depo- 
larizer may  itself  form  the  cathode,  if  it  be  a  solid  conduct- 
ing material,  the  office  of  the  cathode  being  primarily  to 
establish  a  connection  between  the  electrolyte  and  the  exter- 
nal circuit. 

2606.  Cells  in  Whicli  an  Elementary  Substance 
Is  Applied  to  the  Cathode,  Acting  as  a  Depolarizer. — 

This  substance  may  be  applied  mechanically  or  chemically. 
In  the  former  case,  the  body,  in  the  form  of  a  gas  or  liquid^ 
is  made  to  appear  at  the  cathode  by  pumping  or  forcing  it 
to  that  place  from  some  external  source  of  supply.  In  the 
chemical  method,  the  cathode  is  surrounded  by  solid  or 
liquid  substances,  which  by  their  action  on  each  other 
evolve  some  elementary  body  which  combines  with  the  free 
element  of  the  decomposed  electrolyte. 


1714  BATTERIES. 

This  is  distinct  from  tlie  action  of  cells  with  a  liquid  or  a 
solid  depolarizer,  as  the  production  of  the  elementary  de- 
polarizing body  substance  is  independent  of  the  electrical 
action  of  the  cell,  going  on  all  the  time,  whether  the  cell  is  in 
tise  or  not,  variations  in  the  current  output  of  the  cell  having 
no  influence  on  its  production. 

Voltaic  cells  are  ordinarily  classed  as  "  single-fluid  "  and 
*"' two-fluid "  cells ;  but  as  such  a  classification  has  little 
reference  to  this  principle  of  operation,  it  will  not  be  used 
in  this  discussion.  The  number  of  different  kinds  of  cells 
that  have  been  made  is  very  large  indeed,  but  they  can  all 
be  subdivided  into  one  of  these  general  classes.  Only  a  few 
typical  cells  of  each  class  will  be  described. 


CELLS    WITH    A   NON-DEPOLARIZING 
ELECTROLYTE. 

2607.  This  class  of  cells  includes  the  cells  of  the 
Volta  type,  which  consists  generally  of  an  electrolyte  of 
acid  or  saline  solution,  into  which  are  placed  two  or  more 
plates  of  metal,  one  of  which  (usually  of  zinc)  is  acted  on  by 
the  electrolyte. 

2608.  A  simple  form  of  this  cell  is  illustrated  in  Art. 
2238.  Its  materials  are  zinc,  dilute  sulphuric  acid,  and 
copper,  which  give  an  E.  M.  F.  of  about  .9  volt. 

Many  modifications  of  the  form  of  this  type  of  cell  have 
been  suggested  and  used,  such  as  making  the  elements  in 
strips  and  rolling  them  around  each  other  in  a  helical  form, 
with  insulating  material  between,  etc. ;  but  all  are  open  to 
the  objection  of  rapid  polarization. 

2609.  In  place  of  copper  as  a  cathode  many  other 
elements  have  been  used,  notably  the  Smee  cell,  using 
platinum  or  platinized  silver,  and  cells  of  various  makes  in 
which  the  cathode  is  of  iron. 

In  cells  of  this  and  other  types,  impurities  in  the  zinc  set 
up  local  actions,  which  diminish  the  E.  M.  F.  of  the  cell  and 
cause  a  wasting  of  the  zinc.     These  local  actions  are  almost 


BATTERIES.  1715 

wholly  prevented  by  amalgamating  the  zinc,  which  is  usually 
done. 

If  a  good  quality  of  drawn  or  rolled  zinc  is  used,  this  pre- 
caution is  hardly  necessary. 

261 0.  Not  long  after  the  first  use  of  the  zinc,  sulphuric 
acid,  and  copper  battery,  it  was  found  that  the  copper  or 
other  metallic  cathode  could  be  advantageously  replaced 
with  porous  carbon,  and  many  cells  were  so  constructed. 
The  E.  M.  F.  of  such  a  cell  is  about  1.35  volts  ordinarily. 
To  prevent  the  electrolyte  from  becoming  exhausted  too 
quickly,  there  is  sometimes  placed  in  the  cell  a  porous 
earthenware  pot  or  cup,  filled  with  strong  sulphuric  acid.  As 
the  dilute  acid  outside  the  porous  cup  becomes  weaker,  the 
stronger  acid  oozes  through  the  sides  of  the  porous  cup  and 
keeps  up  its  strength.  In  some  instances  the  carbon 
cathode  has  itself  formed  the  porous  cup.  An  objection  to 
the  use  of  porous  cups  in  this  type  of  cell  is  that  its  pores 
are  liable  to  become  clogged  by  deposits  of  zinc  sulphate 
from  the  solution. 

2611.  Other  acid  electrolytes  have  been  used  in  this 
type  of  cell.  With  either  nitric  or  hydrochloric  acids 
(diluted)  the  E.  M.  F.  is  not  sensibly  different  from  that 
with  sulphuric  acid  as  the  electrolyte. 

2612.  Of  the  saline  electrolytes,  the  best  exciting 
liquid  is  considered  to  be  a  solution  of  ammonium  chloride 
(sal  ammoniac).  The  E.  M.-  F.  of  a  zinc,  ammonium  chlo- 
ride, and  carbon  cell  is  about  1.15  volts. 

2613.  There  are  a  great  number  of  cells  of  this  type  in- 
use  for  ringing  bells,  gas  lighting,  and  doing  other  intermit- 
tent work.  They  are  all  alike  in  principle,  but  their 
mechanical  construction  differs  somewhat.  In  the  Law 
open-circuit  cell,  the  carbon  electrode  is  in  the  form  of  a 
hollow  cylinder,  enclosing  a  smaller  hollow  cylinder,  each 
with  a  wide  slit  in  one  side.  These  cylinders  hang  vertically 
in  the  electrolyte,  and  the  zinc  hangs  in  the  space  formed  by 
the  slits  in  the  side,  being  suspended  from  the  cover  of  the 


1716  BATTERIES. 

cell.      This  is  an  excellent  form  of  cell,  being  well  worked 
out  in  its  mechanical  details. 

2614.  In  the  Little  Giant  cell,  the  hollow  carbon 
cylinder  is  continuous,  except  for  a  hole  in  the  side  for  the 
circulation  of  the  electrolyte,  and  the  zinc,  in  the  form  of  a 
rod,  is  suspended  in  the  center  of  the  carbon  cylinder.  The 
top  of  the  cylinder  is  extended  to  form  the  cover  of  the  cell, 
and  the  zinc  is  insulated  from  it  by  a  porcelain  bushing. 

2615.  The  Hercules  cell  employs  a  corrugated  solid 
carbon  cylinder,  the  zinc  element  being  made  of  sheet  zinc 
bent  into  a  cylinder  surrounding  the  carbon. 

2616.  Many  other  forms  of  carbon  or  zinc  elements 
may  be  and  are  used.  The  particular  shape  of  the  carbon 
has  comparatively  little  to  do  with  the  satisfactory  working 
of  the  cell,  care  and  good  design  in  the  construction  being 
more  important.  The  element  should  be  of  such  shape  as 
not  to  be  easily  broken  in  transit,  and,  being  usually  molded 
into  shape  under  pressure,  should  be  of  such  proportions 
that  it  is  cheap  to  make. 

2617'.  In  all  the  cells  of  this  type  the  carbon  is  made 
as  porous  as  possible,  and  of  such  shape  that  the  surface 
exposed  to  the  liquid  is  very  large  compared  with  the  sur- 
face of  the  zinc.  Thus,  the  average  area  of  the  internal 
circuit  of  the  cell  is  made  large,  and  at  the  same  time  ad- 
vantage is  taken  of  the  slight  depolarization,  occurring  with 
a  porous  carbon  of  large  surface,  due  to  the  oxygen  which 
porous  carbon  absorbs  from  the  air,  with  which  some  of  the 
evolved  hydrogen  combines.  The  E.  M.  F.  of  this  type  of 
cell  is,  therefore,  slightly  higher  than  those  which  employ 
a  non-oxidizable  metallic  cathode,  such  as  platinum.  This 
depolarizing  action  takes  place  sloAvly,  and,  therefore,  hy- 
drogen will  form  on  the  cathode  if  a  considerable  current  be 
taken  from  the  cell,  thus  increasing  the  internal  resistance. 
In  intermittent  work  this  is  not  objectionable,  as  the  hydro- 
gen is  soon  absorbed  when  the  external  circuit  is  opened. 


BATTERIES.  1717 

2618.  Another  salt  which  has  been  much  used  in  solu- 
tion as  an  electrolyte  is  sodium  chloride  (common  salt). 
The  heat  of  formation  of  sodium  chloride  being  greater  than 
that  of  ammonium  chloride,  the  energy  required  to  decom- 
pose the  electrolyte  is  greater;  therefore,  the  E.  M.  F.  of 
cells  using  this  electrolyte  is  slightly  lower,  that  of  a  zinc, 
sodium  chloride,  and  carbon  cell  being  about  1.08  volts. 

However,  this  electrolyte  being  very  cheap  and  of  com- 
mon occurrence,  many  makers  of  batteries  have  employed 
it.  It  has  also  been  proposed  to  use  sea-water  as  an  electro- 
lyte, by  placing  in  the  ocean  immense  plates  of  zinc  and 
copper  or  carbon.  This  has  never  been  commercially  ac- 
complished, for  the  consumption  of  zinc  makes  the  cost  of 
the  electrical  energy  too  great  for  this  method  to  compete 
with  others  now  in  use. 

2619.  Electrical  buoys  have  been  constructed,  in  which 
plates  of  carbon  or  copper  and  zinc  enter  or  leave  the  water 
as  the  buoy  is  rocked  by  the  waves,  thus  causing  a  light  to 
flash  or  a  bell  to  ring  intermittently. 

2620.  Various  other  salts  in  solution  have  been  used 
as  electrolytes,  such  as  ammonium  nitrate,  alum,  potassium 
sulphate,  zinc  sulphate,  zinc  chloride,  potassium  hydrate 
(caustic  potash),  etc. 

The  E.  M.  F.  of  cells  using  solutions  of  these  various 
salts  as  electrolytes  may  be  found  from  the  values  given  in 
Table  93. 

2631.  The  effect  of  substituting  various  metals  for  the 
zinc  in  this  type  of  cell  may  be  found  from  Table  92,  which 
gives  the  E.  M.  F.  of  the  action  of  dilute  sulphuric  acid  on 
various  metals.  The  values  given  in  this  table  may  be 
taken  for  the  E.  M.  F.  of  cells  using  a  platinum  or  carbon 
cathode;  if  other  metals  which  appear  in  the  table  be  used 
as  the  cathode,  the  E.  M.  F.  of  the  action  of  the  acid  upon 
them  must  be  subtracted  to  get  the  E.  M.  F.  of  the  cell. 
(See  Art.  2590.)  With  other  electrolytes,  the  substitu- 
tion of  other  metals  for  zinc  reduces  the  E.  M.  F.  in  about 
the  same  proportion  as  in  the  table. 


1718 


BATTERIES. 


TABLE    92. 

E.  M.  F.   OF  THE  FORMATION   OF   VARIOUS 
SULPHATES. 


Metal. 

Formula  of 
Sulphate. 

E.  M.  F. 
Volts. 

Potassium 

ZnSO^ 
CdSO, 
PbSO^ 

FcSO, 

CuSO, 

Ag.^0, 

None 

2  35 

Zinc 

1  35 

Cadmium 

1.05 

Lead 

.90 

Tin 

88 

Iron 

.83 

Aluminum 

.70 

CoDoer ,  .  . .  . 

.47 

Silver 

.30 

Platinum 

.00 

TABLE    93. 

E.  M.  F.   OF  ZINC   (PURE)  WITH   VARIOUS   ELECTROLYTES. 


Electrolyte. 
Acids. 

E.  M.  F. 
Volts. 

Electrolyte. 
Saline  Solutions. 

E.  M.  F. 
Volts. 

HSO, 

1.35 

1.40 
1.43 

NaCl 

1  08 

HCl 

ZllSO     

1  32 

HNO, 

NH  CI. 

1  15 

NaOH 

1.35 

KOH 

1  38 

Ordinary //„  (9 

0.90 

CELLS  WITH  A  DEPOLARIZING  ELECTROLYTE. 
2622.  The  best  known  cells  of  this  type  are  the  so- 
called  bichromate  cells.  These  consist,  broadly,  of  a  zinc- 
carbon  couple,  with  an  electrolyte  composed  of  a  solution  of 
some  acid  or  other  exciting  liquid,  mixed  with  a  proportion 
of  the  bichrojnate  salts  of  some  metal.  The  bichromate 
salts  are  a  peculiar  series  of  salts  formed  by  the  oxide  of 


BATTERIES. 


1719 


chromium  having  the  formula  Cr^O^,  which  is  an  unstable 
oxide,  appearing  only  in  combination  with  some  other  metal, 
such  as  potassium  or  sodium,  forming  the  bichromate  salts 
of  those  metals.  The  mixture  usually  employed  as  an  elec- 
trolyte is  sulphuric  acid  and  potassium  bichromate,  K„Cr^O^, 
although  sodium  bichromate,  Na^Cr^O^,  is  somewhat  supe- 
rior for  the  purpose,  which  is  to  act  as  a  depolarizer.  This 
office  the  bichromate  salts  perform  perfectly,  as  they 
have  a  large  proportion  of  oxygen,  as  is  seen  from  their 
formulas;  consequently,  the  hydrogen  liberated  by  decom- 
position of  the  electrolyte  is  consumed  as  fast  as  generated, 
forming  water  and  a  salt  known  as  chrome  alum,  which 
forms  in  crystals  of  a  purplish  color.  This  results  in  a  high 
E.  M.  F.  (usually  about  2  volts). 

2623.  The  chemical  actions  in  this  class  of  cells  are 
complicated;  one  result  is  the  formation  of  chromic  acid  by 
the  action  of  the  acid  in  the  electrolyte  on  the  K^Cr^O^, 
which  will  slowly  attack  the  zinc  whenever  in  contact  with 
it,  whether  there  be  any  current  flowing  or  not.  This  leads 
to  the  device — which  is  almost  universally  adopted — -of  lift- 
ing the  anode,  or  both  elements,  from  the  liquid  when  the 
cell  is  not  in  use.  Cells  which  are  in  continuous  use  are 
liable  to  have  their  internal  resistance 
increased  by  a  deposit  of  the  crystals  of  ^^-* 
chrome  alum  on  the  cathode,  these  crys- 
tals being  poor  conductors.  In  certain 
forms  of  cells  the  construction  is  such 
that  this  is  not  liable  to  occur. 

2624.  Afamiliar  type  of  bichromate 
cell  is  the  Grenet  cell,  shown  in  Fig. 
1038,  which  consists  of  a  bottle-shaped 
glass  jar  with  a  hard  rubber  or  porcelain 
cover.  From  this  cover  two  flat  carbon 
plates  C,  C  are  suspended,  parallel  to 
and  a  short  distance,  from  each  other,  as 
shown;  between  them  hangs  a  zinc  plate 
Z  supported  by  a  sliding  rod  R,  which  fig.  loas. 


1720  BATTERIES. 

may  be  drawn  up  until  the  zinc  is  entirely  out  of  the  liquid; 
it  is  held  in  any  position  by  the  thumb-screw  T.  On  the  top 
of  the  brass  rod  is  a  binding-post  B^,  the  other  terminal  of 
the  cell  being  the  binding-post  B^  which  is  connected  to  the 
two  carbon  plates. 

The   electrolyte    is  composed    of    3    parts    of    potassium 
bichromate,   dissolved    in    18    parts    of    water,  to    which    is 
added  4  parts  of  sulphuric  acid. 
.     The  E.  M.  F.  of  such  a  cell  is  1.93  to  2  volts. 

At  ordinary  temperatures,  variations  in  the  proportion  of 
bichromate  in  the  solution,  within  moderate  limits,  do  not 
vary  the  E.  M.  F.  or  the  internal  resistance  very  much. 
Variations  in  temperature  vary  the  internal  resistance,  but 
not  the  E.  M.  F.,  the  internal  resistance  decreasing  as  the 
temperature  increases.  With  the  above  proportion  of  sul- 
phuric acid  and  bichromate  in  the  solution,  the  sulphuric 
acid  is  first  exhausted.  Theoretically,  for  an  equal  life  of 
both  substances  in  the  electrolyte,  the  correct  proportions 
should  be 


z-  r    r^        o  a  I  P^""^^  ^^  weight, 

which  proportion  is  often  used.  In  fact,  however,  it  is  more 
necessary  to  keep  up  the  strength  of  the  depolarizer,  that 
is,  the  bichromate,  so  the  first  given  proportion  will  really 
give  better  results. 

2625.  A  great  variety  of  batteries  of  this  type  has 
been  made,  especially  abroad,  where  they  are  called  Pog- 
gendorfs  cell;  they  do  not  differ  in  principle  or  material 
from  the  Grenet  cell,  but  in  inechanical  details  are  more 
suited  to  general  work.  They  are  usually  built  with  several 
cells,  the  various  elements  being  connected  in  series  to  give 
an  E.  M.  F.  of  6  to  10  or  more  volts.  All  the  elements  are 
simultaneously  raised  out  of  or  lowered  into  the  liquid  by 
a  lever  or  windlass  arrangement,  as  shown  in  Fig.  1039, 
which  represents  a  battery  of  five  cells  all  alike.  The  ele- 
ments are  of  zinc  and  carbon,  there  being  three  plates  of 
zinc,  Z,  and  four  of  carbon,  (7,  in  each  cell.     The  plates  are 


BATTERIES. 


1721 


all  suspended  from  a  wooden  cross-bar,  so  that  they  may  be 
simultaneously  raised  or  lowered  by  winding  or  unwinding 


Fig.  1039. 
the  chains  H,  H  upon  the  rod  R^  which  is  turned  by  means 
of  the  crank  K. 

The  elements  may  thus  be  raised  from  the  liquid  con- 
tained in  the  jars  J  when  the  cells  are  not  in  use.  The 
elements  of  each  cell  are  provided  with  two  binding-posts 
B,  B,  one  of  which  is  connected  to  the  carbon  and  the  other 
to  the  zinc  plates.  The  various  cells  may  then  be  used 
separately,  or  connected  together  in  parallel  or  in  series, 
as  desired. 

2626.  An  ingenious  arrangement  of  bichromate  cells 
for  cautery  work  is  that  due  to  Chardin.  In  his  battery 
the  elements  are  normally  held  out  of  the  liquid  by  a 
spring;  by  pressing  a  foot  lever  they  may  be  gradually 
lowered  into  the  liquid. 

When  just  the  ends  of  the  elements  are  in  the  liquid,  the 
internal  resistance  of  the  battery  is  considerable;  but  as 
the  elements  are  lowered,  this  resistance  decreases  largely. 


1723  BATTERIES. 

By  varying  the  distance  which  the  pressure  on  the  foot 
lever  causes  the  elements  to  dip  into  the  liquid,  a  sensitive 
and  easily  managed  method  of  control  of  the  output  of  the 
battery  is  secured. 

■  2627.  Another  type  of  bichromate  cell  consists  of  a 
closed  vessel  divided  into  two  parts  by  a  horizontal  per- 
forated partition.  In  one  part  the  zinc  and  carbon  elements 
are  located.  Enough  liquid  to  fill  one  of  the  parts  of  the 
vessel  is  introduced;  when  the  vessel  is  standing  on  one 
end,  all  the  liquid  is  below  the  partition  and  the  elements 
above,  and  in  order  to  render  the  cell  active,  it  is  only 
necessary  to  turn  the  vessel  completely  over,  when  the 
liquid  flows  through  the  perforated  partition  and  comes  in 
contact  with  the  zinc  and  carbon. 

2628.  Among  the  cells  which  may  be  said  to  belong  to 
this  class  is  a  type  of  cell  in  which  no  free  hydrogen  or 
other  gas  is  evolved  in  the  decomposition  of  the  electrolyte. 
Such  electrolytes,  which  might  more  properly  be  called 
non-polarizing,  are  the  solutions  of  some  of  the  salts  of 
metals  having  more  than  one  valency.  The  salt  containing 
the  greater  amount  of  the  non-metallic  element  (the  zV  salt) 
is  used  as  the  electrolyte;  on  being  decomposed,  a  salt  of 
the  metal  of  the  anode  is  formed  with  a  part  of  its  non- 
metallic  element,  and  the  remainder  is  recombined  to  form 
the  salt  having  the  lesser  proportion  of  the  non-metallic 
element  (the  ons  salt). 

2629.  An  example  of  this  type  of  cell  is  the  Pabst 
cell,  in  which  wrought  iron  and  carbon  are  used  as  elements, 
and  a  solution  of  ferric  chloride  as  the  electrolyte.  The 
ferric  chloride  is  decomposed  into  ferrous  chloride  and  free 
chlorine ;  the  latter  unites  with  the  iron  anode,  resulting  in 
an  E.  M.  F.  of  .78  volt. 

2630.  Similar  cells  are  also  made,  using  a  solution  of 
ferrous  sulphate  as  an  electrolyte,  the  action  being  similar. 
There  are  other  salts,  with  solutions  of  which  zinc  will 
combine  without  hydrogen  being  released,  such  as  sulphite 


BATTERIES.  1723 

of  potassium  or  of  sodium,  and  non-polarizing  cells  are 
constructed,  employing  solutions  of  these  salts  as  elec- 
trolytes. 

2631.  Most  single  fluid  cells  in  which  the  electrolyte 
is  depolarizing  are  open  to  the  objection  that  the  zinc  is 
attacked  by  the  electrolyte  at  all  times,  whether  the  exter- 
nal circuit  be  closed  or  not;  besides  this,  with  the  exception 
of  the  bichromate  cells,  the  materials  of  the  electrolyte  are 
usually  expensive,  and  not  readily  obtainable,  and  the  com- 
mercial use  of  such  cells  is  limited. 


CELLS    WITH    A    LIQUID    DEPOLARIZER. 

2632.  Nitric  acid,  being  rich  in  oxygen,  is  largely 
used  as  a  depolarizing  liquid  in  this  class  of  cells. 

Its  use  is  objectionable  from  the  fact  that  when  deprived 
of  a  part  of  its  oxygen,  it  gives  off  a  gas,  nitric  oxide, 
which,  on  combining  with  the  oxygen  of  air,  becomes  nitro- 
gen peroxide,  NO^,  a  disagreeable  and  even  dangerous  cor- 
rosive gas;  consequently,  the  best  of  ventilation  is  essential 
where  cells  with  this  depolarizer  are  used. 

2633.  The  principal  cells  using  this  depolarizer  are  the 
Grove  and  Bunsen  cells,  and  some  of  their  derivatives. 
In  the  Grove  cell  the  positive  element  is  zinc;  the  negative, 
platinum.  The  platinum  element  is  placed  inside  a  porous 
cup  and  surrounded  with  nitric  acid;  outside  the  porous  cup 
is  the  exciting  liquid,  sulphuric  acid  diluted  with  water. 
The  E.  M.  F.  of  the  Grove  cell  is  1.9  volts  at  ordinary 
temperatures. 

2634.  The  Grove  cell  is  a  very  old  type,  and  has  been 
made  in  many  forms,  but  the  expense  of  using  the  platinum 
element  has  led  to  the  adoption  of  the  Bunsen  cell,  which 
substitutes  a  carbon  element  for  the  platinum.  With  com- 
mercial nitric  acid,  specific  gravity  about  1.33,  the  E.  M.  F. 
of  the  Bunsen  cell  is  1.89  volts  ordinarily;  if  pure  (fuming) 
nitric  acid,   specific  gravity  1.53,  be  used,  the  E.  M.  F.  is 


1724  BATTERIES. 

increased  to  about  1.96  volts.     About  .35  volt  is  due  to  the 
action  of  the  depolarizer. 

2635.  Variations  in  the  density  of  the  nitric  acid  thus 
affect  the  E.  M.  F.  of  the  cell  only  slightly,  until  the  specific 
gravity  of  the  solution  falls  to  about  1.23;  but  at  a  density 
below  this  the  acid  has  little  or  no  effect  as  a  depolarizer, 
although  the  liquid  still  contains  about  oOfo  of  nitric  acid. 

As  the  commercial  acid  is  most  frequently  used  in  the  cell, 
only  a  small  proportion  of  water  is  required  to  dilute  it  to  a 
point  where  it  can  not  be  used.  In  fact,  where  commercial 
acid  is  used,  only  about  13^  of  the  actual  amount  of  the  pure 
acid  in  the  solution  can  be  utilized,  if  nitric  acid  alone  be 
the  depolarizer. 

The  water  formed  at  the  cathode  by  the  process  of  de- 
polarization, therefore,  is  disadvantageous  on  account  of  its 
dilution  of  the  depolarizer. 

Several  investigators  have  mixed  sulphuric  acid  with  the 
nitric,  in  various  proportions,  with  good  results.  Sulphuric 
acid  has  a  strong  affinity  for  water,  and  will  combine  with 
it  in  considerable  quantity ;  consequently,  the  water  formed 
at  the  cathode  is  absorbed  by  the  sulphuric  acid,  leaving  the 
nitric  acid  at  its  full  strength. 

2636.  Variations  in  the  density  of  the  exciting  liquid 
also  affect  the  E.  M.  F.  of  the  cells  to  some  extent,  but  not 
so  much  so  as  variation  in  the  density  of  the  depolarizer. 
The  density  ordinarily  used  is  about  1.09  sp.  gr.  (13^  by 
weight  of  acid).  At  this  point  the  E.  M.  F.  of  the  action  of 
the  exciting  liquid  on  the  zinc  is  about  1.53  volts. 

As  the  action  of  pure  water  alone  on  zinc  will  give  an 
E.  M.  F.  of  about  .9  volt,  variations  of  the  density  of  the 
exciting  liquid  from  13^  (by  weight)  of  acid  down  to  pure 
water  will  reduce  the  E.  M.  F.  about  .6  volt.  Increasing 
the  density  of  the  liquid  to  about  1.23  gives  a  maximum 
E.  M.  F,  (of  the  action  of  the  acid  on  the  zinc  only)  of  about 
1.6  volts;  any  further  increase  in  the  density  does  not  in- 
crease the  E.  M.  F.  appreciably.  To  obtain  the  E.  M.  F.  of 
the  cell,  to  the  above  figures  should  be  added  the  E.  M.  F. 


BATTERIES.  1725 

due  to  the  action  of  the  depolarizer,  about  .35  volt,  as  stated 
above. 

It  is  somewhat  difficult  to  maintain  sulphuric  acid  which 
has  free  access  to  the  air  at  a  density  much  above  about  1.10, 
on  account  of  the  absorption  of  water  from  the  air  by  the 
acid,  and  acid  of  about  this  density  is  ordinarily  used. 

2637.  The  proportions  of  the  two  acids  in  the  cells  are 
about  3  of  exciting  liquid  to  1  of  depolarizer,  the  depolarizer 
being  of  a  specific  gravity  of  about  1.33;  with  these  propor- 
tions the  cell  will  maintain  its  E.  M.  F.  (within  about  lOfo) 
for  several  days  on  a  closed  circuit. 

The  average  internal  resistance  (as  ordinarily  constructed) 
is  about  2  ohms. 

2638.  Many  modifications  of  the  Grove  and  Bunsen 
cells  have  been  made,  some  consisting  merely  in  changes  in 
the  mechanical  arrangement  of  the  parts,  others  substituting 
various  depolarizers,  exciting  liquids,  or  elements. 

For  example,  a  carbon  cup  fitted  with  a  tight  cover  has 
been  used  as  cathode.  On  this  being  filled  with  nitric  acid, 
the  gas  given  off  by  the  acid  produces  a  pressure  inside  the 
cup,  which  forces  the  acid  out  through  the  pores  of  the  car- 
bon to  the  surface,  where  its  depolarizing  action  takes  place. 
This  suppresses  a  part  of  the  disagreeable  fumes  of  the  acid. 
To  accomplish  this  same  result,  it  has  been  proposed  to  cover 
the  cell  with  an  inverted  vessel  containing  scrap  tin,  which 
will  absorb  the  fumes.  A  layer  of  turpentine  floating  on  the 
acid  will  prevent  a  large  part  of  the  fumes  from  being  given 
off,  as  they  combine  with  the  turpentine. 

2639.  When  iron  or  steel  is  placed  in  strong  nitric  acid 
it  is  not  attacked,  although  this  acid  is  a  powerful  oxidizing 
agent;  but  when  the  acid  is  diluted  to  about  1.20  sp.  gr.,  or 
lower,  the  iron  is  strongly  attacked. 

Consequently,  with  a  strong  solution  of  nitric  acid"  as  a 
depolarizer,  iron  (usually  cast  iron)  may  replace  the  carbon 
element  of  the  Bunsen  cetl,  with  good  results,  the  E.  M.  F. 
being  about  1.7  volts.  Care  must  be  taken,  however,  that 
the  density  of  the  depolarizer  does  not  fall  too  low,  or  the 


1726 


BATTERIES. 


negative  element  will  be  consumed.  In  fact,  a  cell  of  this 
class  may  be  constructed  with  only  iron  and  nitric  acid  as 
elements,  in  the  following  order:  Iron  (anode),  dilute  nitric 
acid,  porous  cup,  strong  nitric  acid,  and  iron  (cathode). 

2640.  A  cell  similar  to  the  foregoing,  except  that  the 
negative  element  is  carbon  instead  of  iron,  known  as  the 
Maeche  cell,  gives  an  E.  M.  F.  of  1.5  volts,  and  has  the  ad- 
vantage of  giving  off  a  much  less  quantity  of  nitrous  vapor 
than  the  Bunsen.  By  substituting  ordinary  water  for  the 
dilute  acid  in  the  Maeche  cell,  the  E.  M.  F.  is  reduced  to 
about  1.2  volts;  but  owing  to  the  difference  in  specific  grav- 
ity of  the  two  liquids  (nitric  acid  and  water),  they  soon  mix 
somewhat  through  the  walls  of  the  porous  cup. 

2641.  The  E.  M.  F.  of  this  type  of  cell  is  really  gener- 
ated in  two  parts:  one  at  the  surface  of  the  anode,  due  to 
the  action  of  the  electrolyte  on  the  anode,  and  the  other  at 
or  near  the  cathode,  due  to  the  action  of  the  depolarizing 
liquid  on  the  hydrogen  evolved.  (See  Art.  2590.)  Vary- 
ing the  material  of  the  anode  or  the  electrolyte  will  then 
affect  that  part  of  the  E.  M.  F.  just  as  in  a  cell  of  the  class 
given  in  Art.  2602,  and  the  amount  by  which  the  E.  M.  F. 
is  reduced  or  increased  may  be  found  from  the  values  given 
in  Tables  92  and  93,  making  due  allowance  for  the  E.  M.  F. 
due  to  the  depolarizing  action.  The  effect  on  the  E.  M.  F. 
of  varying  the  depolarizer  may  likewise  be  calculated  from 
the  values  given  in  Table  94. 

TABLE  94. 

DEPOLARIZIIVG  EFFECT   OF   VARIOUS   SUBSTANCES. 


Substance. 
Solids. 

E.  M.  F. 
Volts. 

Substance. 
Liquid. 

E.  M.  F. 
Volts. 

yJ/;/ 6*2  (ordinary) 

Pb  0 

.33 
.81 

HNO^       (c  o  n  c  e  n- 
trated) 

.35 

•^  "i^x 

H  CrO   

.47 

■'■■L^^i  ^ ^ 

CI  gas  dissolved   in 
water 

.04 

BATTERIES.  mi 

2'^4:2>.  The  foregoing  values  for  the  E.  M.  F.  in  Tables 
92,  93,  and  94  are  about  the  average  of  the  somewhat  vary- 
ing results  of  different  experimenters. 

The  values  also  vary  somewhat  with  different  tempera- 
tures and  degrees  of  concentration  of  the  liquids;  they  will 
be  seen  to  be  approximately  correct  if  compared  with  exist- 
ing cells. 

It  will  be  seen  from  this  table  that  either  chromic  acid  or 
chlorine  water  (chlorine  gas  dissolved  in  water)  used  as  a 
depolarizer  would  give  a  higher  E.  M.  F,  than  nitric  acid; 
but  as  these  liquids  decompose  in  the  presence  of  air,  they 
can  not  be  commercially  used,  just  as  in  the  case  of  sodium 
or  potassium  as  anodes.      (See  Art.  2599.) 

2643.  Another  important  type  of  cell  of  this  class  is 
the  bichromate  cell,  which  differs  from  that  described  in 
Art.  2603,  in  that  the  bichromate  solution  is  not  mixed 
with  the  electrolyte,  but  is  separated  from  it  by  a  porous 
partition,  with  the  effect  that  the  zinc  is  not  seriously  attacked 
on  open  circuit.  As  to  the  E.  M.  F.,  chemical  action,  etc., 
this  type  is  not  sensibly  different  from  the  bichromate  cells 
described  in  Art.  2603. 

The  bichromate  solution  is  usually,  with  the  cathode, 
placed  in  the  outer  vessel,  the  zinc  and  exciting  liquid  being 
inside  the  porous  cup;  the  exciting  liquid  being  usually 
sulphuric  acid  diluted  with  water  to  about  1.10  sp.  gr. , 
although  solutions  of  sodium  chloride  or  ammonium  chloride 
are  used. 

2644.  The  depolarizing  liquid  is  usually  of  the  com- 
position given  in  Art.  2624,  under  the  name  electropoion 

fluid.  A  bichromate  mixture  is  prepared  by  dealers  in 
battery  material,  as  follows  (all  parts  by  weight) :  Sulphuric 
acid,  2  parts,  is  mixed  with  water,  4  parts;  in  another  vessel, 
1  part  of  potassium  bichromate  is  dissolved  in  3  parts  of 
boiling  water,  and  while  hot  is  mixed  with  the  liquid  first 
prepared.  This  liquid,  when  cold  and  more  or  less  diluted, 
is  suitable  for  use  in  most  bichromate  cells.  » 


1728 


BATTERIES. 


2645.  The  Fuller  bichromate  cell,  one  form  of  which 
is  represented  in  Fig.  1040,  is  a  very  excellent  cell  of  this 

type,  being  economical  in 
operation.  It  consists  of  a 
glass  jar  containing  the  de- 
polarizer (electropoion  fluid 
diluted  about  one-half),  into 
which  is  hung  the  carbon 
cathode  C.  In  the  center  of 
the  jar  is  placed  the  porous 
cup  P,  into  which  is  poured 
a  little  mercury,  and  the 
zinc,  which  is  in  the  form  of 
a  rod  or  wire  W,  with  a 
conical  lump  Z  cast  on  the 
1:-^  end,  placed  in  position.  The 
mercury  serves  to  keep  the 
zinc  well  amalgamated. 
The  exciting  liquid  is 
Fig.  1040.  either  very  dilute  sulphuric 

acid,  or,  more  commonly,  pure  water.  The  E.  M.  F.  is  2.14 
volts,  and  the  internal  resistance  (of  the  type  shown  in  Fig. 
1039)  usually  about  1  ohm,  depending,  however,  on  the 
thickness  and  character  of  the  porous  cup.  This  type  of 
cell  is  largely  used  for  telegraphic  purposes  in  England. 

2646.  Bichromate  cells  are  often  constructed  in  which 
the  liquids  employed  have  such  a  difference  in  their  specific 
gravities  that  they  may  be  placed  one  over  the  other  in  the 
cell,  no  porous  partition  being  required  to  keep  them  from 
mixing. 

2647.  The  Partz  cell,  one  form  of  which  is  illustrated 
in  Fig.  1041,  is  an  example.  This  cell  is  a  bichromate  cell 
(see  Art.  2643),  which  uses  a  solution  of  sodium  chloride, 
or  of  magnesium  sulphate,  as  an  electrolyte,  surrounding 
the  zinc  Z,  and  a  bichromate  solution  as  a  depolarizer,  sur- 
rounding the  carbon  cathode  C.  The  depolarizer,  having 
a  higher  specific  gravity  than  the  electrolyte,  remains  at  the 


BATTERIES. 


1729 


bottom  of  the  jar,  and  the  two  liquids  are  kept  separate.  As 
the  depolarizer  is  weakened  by  use,  it  is  from  time  to  time 
strengthened  by  the  intro- 
duction of  crystals  in  the 
glass  tube  7",  which  is  sus- 
pended in  the  cell,  having 
a  small  opening  below  the 
normal  level  of  the  bichro- 
mate solution.  The  crys- 
tals used '  are  what  the 
manufacturers  call  sulpho- 
chromic  salt,  which  is 
formed  by  the  action  of 
sulphuric  acid  on  some 
bichromate  solution,  and 
when  dissolved  in  water 
gives  the  same  results  as 
the  electropoion  fluid  (Art. 
2644). 

With  the  cell  shown, 
which  employs  a  6-in.  X 
8-in.  jar,  the  internal  re- 
sistance is  about  1  ohm  with  a  solution  of  magnesium  sul- 
phate, and  about  .5  ohm  with  a  solution  of  sodium  chloride, 
the  E.  M.  F.  being  the  same,  1.9  to  2  volts,  in  either  case. 
This  cell  is  good  for  either  open  or  closed  circuit  work,  as 
the  depolarization  is  very  complete;  at  the  same  time,  the 
local  action  on  open  circuit  is  almost  imperceptible. 

The  chrome  alum  solution  which  forms,  being  heavier 
than  the  bichromate  solution,  descends  to  the  lower  part  of 
the  cell,  so  that  the  crystals  form  beneath  the  carbon  plate, 
which  is  slightly  raised  from  the  bottom  of  the  jar;  conse- 
quently, the  formation  of  these  crystals  does  not  appre- 
ciably increase  the  internal  resistance  of  the  cell. 


Fig.  1041. 


2648.  Another  form  of  gravity  bichromate,  known  as 
the  Kousmine  cell,  has  its  liquids  arranged  in  the  reverse 
order    to    the    above.      The    electrolyte    is    sulphuric    acid 


1730  BATTERIES. 

diluted  to  about  1.15  sp.  gr.  or  less,  and  surrounds  the  zinc 
anode  at  the  bottom  of  the  jar.  The  depolarizer  is  a  very 
■weak  solution  of  potassium  bichromate,  which  floats  on  the 
sulphuric  acid,  being  much  lighter,  and  surrounds  the 
carbon  cathodes  at  the  top  of  the  jar.  The  heavy  solution 
of  chrome  alum  falls  to  the  bottom,  as  in  the  Partz  cell. 
The  E.  M.  F.  and  actions  of  this  cell  are  the  same  as  in 
other  bichromate  cells,  but  its  life  is  not  long,  the  bichro- 
mate solution  being  soon  exhausted  by  use. 

2649.  It  can  be  readily  seen  that  in  cells  of  this  class, 
consisting  of  the  anode,  exciting  liquid,  porous  partition, 
depolarizing  liquid,  and  cathode,  a  great  number  of  differ- 
ent styles  of  cells  may  be  constructed,  by  varying  any  of 
the  four  principal  constituents,  and  a  great  many  such 
variations  have  been  made  or  suggested. 

As  pointed  out  in  Arts.  2599  and  2600,  zinc  is  really 
the  best  and  cheapest  material  for  the  anode;  consequently, 
substituting  other  metals  has  not  usually  benefited  the  cell, 
except  in  special  cases.  The  effect  on  the  E.  M.  F.  of  such 
substitution  may  be  readily  found  from  Table  92,  as  before. 

Great  varieties  of  solutions  have  been  used  as  electrolytes 
or  depolarizing  liquids ;  some  with  good  results,  and  others 
without  apparent  reason,  except  to  make  a  new  cell. 

2650.  M.  D'Arsonval,  a  French  physicist,  has  made  a 
series  of  cells,  in  which,  by  the  action  of  the  two  liquids  upon 
each  other  at  their  junction  in  the  porous  cup,  an  insoluble 
but  conducting  body  is  deposited  in  the  pores  of  the  porous 
cup,  which  prevents  the  gradual  mixing  of  the  liquids  that 
usually  takes  place.  For  example,  one  of  these  cells  is  made 
up  as  follows:  Zinc,  solution  of  sodium  hydrate  (caustic 
soda),  porous  cup,  ferric  chloride,  and  carbon.  The  E.  M.  F. 
of  this  cell  is  about  2.7  volts;  the  action  of  the  hydrogen  on 
the  ferric  chloride  reduces  it  to  ferrous  chloride  and  hydro- 
chloric acid;  at  the  same  time  ferric  hydrate  (which  is  in- 
soluble, but  a  conductor)  is  formed  in  the  pores  of  the 
porous  cup.    ^ 


BATTERIES.  1731 

2651.  Various  chloride  salts  have  been  used  as  depolar- 
izers in  cells  of  this  class,  the  action  being  usually  the 
reduction  of  the  chloride  to  one  containing  a  greater  pro- 
portion of  the  metallic  element,  or  else  the  entire  reduction 
of  the  chloride,  depositing  the  metallic  element  on  the 
cathode;  in  either  case  the  action  of  the  hydrogen  on  the 
free  chlorine  forms  hydrochloric  acid. 

2652.  Many  of  the  nitrate  and  sulphate  salts  have  also 
been  used  as  depolarizing  liquids,  and  with  a  variety  of 
electrolytes,  generally  acid;  but  the  principal  type  of  this 
class  of  cell,  other  than  the  Bunsen  and  the  bichromate,  is 
the  type  which  employs  as  an  electrolyte  a  salt  of  the  metal 
of  the  anode,  and  as  a  depolarizer  a  salt  of  the  metal  of 
the  cathode.  The  depolarizer  is  usually  a  salt  formed  by 
the  same  acid  that  formed  the  electrolyte  salt;  that  is,  if  the 
electrolyte  be  a  sulphate,  the  depolarizer  is  also  a  sulphate, 
etc.  In  this  case  the  action  is  as  follows:  The  passage  of 
the  current  decomposes  both  liquids,  and  the  hydrogen 
from  the  decomposed  water  unites  with  the  non-metallic 
elements  of  the  decomposed  liquids,  forming  the  acid  from 
which  the  salt  was  formed,  the  metallic  element  of  the  de- 
polarizer being  deposited  on  the  cathode;  this  acid  attacks 
the  anode,  reforming  the  salt  of  which  the  electrolyte  is 
composed.  The  electrolyte,  therefore,  is  continually  added 
to,  while  the  depolarizer  is  continually  reduced. 

2653.  Neglecting  the  intermediate  reactions,  which 
generally  do  not  affect  the  E.  M.  P.,  it  is  evident  that  the 
E.  M.  F.  of  this  type  of  cell  is  due  to  the  energy  given  up 
by  the  formation  of  the  salt  of  which  the  electrolyte  is  com- 
posed, less  the  energy  required  to  decompose  the  salt  of 
which  the  depolarizer  is  composed.  Now,  whatever  may  be 
the  actual  energy  of  the  formation  of  the  various  salts,  the 
difference  between  the  energies  of  formation  of  the  same  salts 
of  any  two  metals  is  the  same,  whatever  the  particular  salt 
may  be ;  for  example,  the  difference  between  the  heat  of  for- 
mation of  zinc  sulphate  and  that  of  copper  sulphate  is  the 


1732  BATTERIEa 

same  as  the  difference  between  the  heats  of   formation  of 
zinc  nitrate  and  copper  nitrate. 

2654.  It  naturally  follows,  that  with  given  metals  for 
the  anode  and  cathode,  the  E.  M.  F.  should  be  the  same, 
whatever  salt  of  the  two  metals  be  used  as  electrolyte  and 
depolarizer,  respectively.  This  is  borne  out  in  practice,  as 
experiments  have  shown  the  E.  M.  F.  under  these  circum- 
stances to  be  practically  the  same. 

In  order,  then,  to  obtain  a  high  E.  M.  F.,  it  is  necessary 
to  use  as  an  anode  a  metal  whose  salts  have  a  high  heat  of 
formation,  and  as  a  cathode  a  metal  whose  salts  have  a  low 
heat  of  formation,  just  as  in  the  other  classes  of  cells. 

For  commercial  use,  the  same  considerations  apply  as  to 
the  other  classes;  that  is,  the  materials  used  in  the  cell 
must  be  easily  and  cheaply  obtained,  even  if  they  do  not 
result  in  the  highest  possible  E.  M.  F.  The  cells  which 
best  realize  this  condition  are  the  Daniell  cell  and  its 
derivatives. 

2655.  The  Daniell  cell  uses  for  the  anode,  zinc;  for 
the  electrolyte,  a  solution  of  (usually)  zinc  sulphate,  ^;25' (9^; 
for  the  cathode,  copper;  and  for  the  depolarizer,  a  solution 
of  copper  sulphate,  CitSO ^.  Sometimes,  in  setting  up  the 
cell,  dilute  sulphuric  acid  is  used  instead  of  the  zinc  sulphate, 
but  this  soon  forms  a  solution  of  zinc  sulphate;  hence,  the 
result  is  the  same  as  if  the  zinc  sulphate  were  used  origi- 
nally. The  E.  M.  F.  of  the  Daniell  cell  is  given  several 
values  by  different  investigators,  ranging  from  1.059  to  1.079 
volts.  The  London  Post  Office  uses  this  cell  as  a  standard, 
and  calls  its  E.  M.  F.  1.07  volts. 

The  original  form  of  the  Daniell  cell  consisted  of  a  glass 
jar,  into  which  the  zinc,  in  the  form  of  a  cylinder,  was  placed. 
Inside  the  zinc  was  a  porous  cup  containing  the  cathode,  a 
strip  of  sheet  copper.  The  porous  cup  was  filled  with  the 
CuSO ^  solution  and  the  outer  jar  with  the  ZnSO^  solution. 

2656.  To  prevent  the  gradual  weakening  of  the  depo- 
larizer, it  is  usual  to  put  a  considerable  amount  of  copper 
sulphate  crystals  (commonly  known  as  blue  vitriol)  into  the 


BATTERIES. 


1733 


porous  cup.  As  the  liquid  weakens,  the  crystals  are  grad- 
ually dissolved.  Several  modifications  of  the  form  of  the 
original  Daniell  cell  are  in  use,  many  of  them  designed  to 
keep  up  the  supply  of  copper  sulphate  as  it  is  weakened. 

265T.  One  such  design,  known  as  the  globe  or  bal- 
loon cell,  is  shown  in  Fig.  1042,  where  Z  is  the  zinc  anode, 
P  the  porous  cup,  in  which  is 
the  copper  cathode  C.  To  keep 
up  the  strength  of  the  depolar- 
izer, a  glass  globe  G  is  filled 
with  crystals  of  copper  sulphate 
vS"  and  a  little  water,  in  which--;_ 
the  copper  sulphate  gradually 
dissolves  ;  the  solution,  being 
heavier  than  the  water,  falls  to 
the  bottom  of  the  neck  of  the 
globe  and  replenishes  the  solu- 
tion in  the  porous  cup.  The 
neck  of  the  globe  extends  down 
into  the  porous  cup  below  the 
level  of  the  liquid,  so  that  the 
water  may  be  retained  in  the 
globe.  The  globe  rests  on  a 
ring  of  some  soft  material  R^ 
making  a  comparatively  tight  joint  between  the  globe  and 
jar,  which  prevents  evaporation  to  a  considerable  extent. 
As  ordinarily  constructed,  the  globe  holds  about  two  pounds 
of  copper  sulphate  crystals,  which  will  usually  last  about  six 
months.  A  cell  similar  to  the  above  is  used  extensively  for 
telegraph  purposes  in  Russia. 

2658.  The  specific  gravity,  at  ordinary  temperature, 
of  a  saturated  solution  of  ZnSO ^  is  about  1.44,  while  that 
of  a  saturated  solution  of  CiiSO^  is  about  1.20;  hence,  if 
saturated  solutions  of  these  salts  are  used,  the  zinc  sulphate 
solution  will  be  considerably  heavier  than  the  other;  it  has 
been  found,  however,  that  the  best  results  are  obtained  from 
a  saturated  solution  of  copper  sulphate,  used  with  a  solution 


Fig.  1042. 


1734  BATTERIES. 

of  zinc  sulphate  diluted  to  a  specific  gravity  of  about  1.10. 
The  considerable  difference  in  weight  between  the  two 
solutions  has  led  to  their  arrangement,  one  over  the  other, 
in  the  cell,  the  heavier  copper  sulphate  being  at  the  bottom. 

2659.  In  the  Hussey  and  the  Gethin  cells  a  porous 
partition  is  used  to  separate  the  two  liquids,  in  the  form  of 
a  porous  cup,  located  in  the  upper  part  of  the  jar.  This 
cup  holds  the  zinc  and  the  electrolyte;  beneath  it  is  the 
copper,  made  in  the  form  of  a  cross  of  sheet  copper,  which 
is  surrounded  by  crystals  of  copper  sulphate. 

2660.  Since  the  proportion  of  the  two  liquids  in  the 
jar  varies  from  time  to  time,  the  porous  partition  does  not 
always  mark  the  point  of  separation  of  the  two  liquids,  and 
it  increases  the  internal  resistance  of  the  cell;  consequently, 
the  batteries  of  this  type  that  are  more  generally  used  are 
those  which  do  not  use  any  porous  partition  at  all,  depend- 
ing on  the  difference  in  the  specific  gravities  of  the  two 
liquids  to  keep  them  apart. 

Such  cells  are  called  gravity  cells,  or  gravity  Daniell 
cells,  and  are  very  extensively  used  for  telegraph  and  fire- 
alarm  work  in  this  country. 

2661.  As  long  as  a  current  is  flowing  through  the  cell, 
the  chemical  action  keeps  the  boundary-line  of  the  two 
liquids  sharply  defined ;  but  when  the  current  ceases  to  flow 
the  solutions  gradually  intermix,  and  the  copper  sulpJiate^ 
coming  in  contact  with  the  zinc  anode,  sets  up  local  actions, 
which  cause  a  deposit  of  copper  on  the  zinc,  and  a  con- 
sumption of  the  zinc  itself.  To  prevent  this  action,  these 
cells  should  be  used  only  on  a  circuit  which  is  closed  practi- 
cally all  the  time,  which  is  the  case  with  telegraph  and  fire- 
alarm  lines. 

2662.  Practically  the  first  cell  of  this  type  to  be  used 
was  the  Callaud  cell,  illustrated  in  Fig.  1043.  In  this  cell 
the  zinc  Z  is  in  the  form  of  a  cylinder,  suspended  by  hooks 
from  the  edge  of  the  jar.  The  copper  (7  is  a  flat  strip  bent 
into  a  circle,  which  rests  on  the  bottom  of  the  jar.     Con- 


BATTERIES. 


1735 


nectlon  ■  is  made  between  it 
means  of  a  wire  JV, 
which  is  insulated 
with  some  rubber 
compound  where  it 
passes  through  the 
liquids.  The  posi- 
tion of  the  two 
liquids  is  shown  in 
the  illustration,  the 
zinc  s  ul  pha  te 
{ZnSOJ  being  at 
the  top,  as  stated. 
This  form  of  cell  has 
been  modified  quite 
largely,  it  being 
now  the  practice  to 
use  lar^e  cast  zincs 


and   the  external  circuit  by 
w       + 


FIG.  1044. 


instead  of  the  cylin» 
der  of  sheet  zinc 
used  in  the  Callaud 
form,  which  allows 
of  a  longer  life  for 
each  cell. 

2663.  The  form 
of  gravity  Daniell 
cell  most  used  in 
this  country  is  the 
familiar  croAvfoot 
cell,  illustrated  in 
Fig.  1044,  where  Z 
is  the  zinc,  from  the 
shape  of  which  the 
cell  gets  its  name; 
C  is  the  copper, 
which  is  connected 
to   the    external 


1736  BATTERIES. 

circuit  by  the  wire  JV,  which  is  insulated  where  it  passes 
through  the  liquid.  When  the  cell  is  set  up  the  copper 
cathode  is  surrounded  with  copper  sulphate  crystals.  The 
standard  form  of  this  cell  is  of  the  following  dimensions: 

Jar,  6  inches  diameter,  8  inches  high.  Copper,  made 
from  three  pieces  of  thin  sheet  copper  2  inches  wide  and 
6  inches  long  riveted  together  in  the  middle;  the  outside 
pieces  are  then  spread  out,  making  the  copper  of  a  six- 
pointed  star  shape.  To  the  middle  strip  is  riveted  a  piece 
of  No.  16  insulated  copper  wire.      (See  Fig.  1044.) 

The  zinc  is  of  the  shape  shown  in  the  illustration,  and 
weighs  3  lb.  About  2  pounds  of  sulphate  of  copper  crystals 
are  required  to  charge  the  cell. 

2664.  The  usual  practice  in  charging  is  to  set  up  the 
elements  in  the  cell,  put  in  the  copper  sulphate,  and  fill  up 
with  clean  water  until  the  zinc  is  covered;  the  cell  is  then 
allowed  to  stand  for  about  24  hours.  By  the  action  of  the 
zinc  on  the  copper  sulphate  solution,  zinc  sulphate  is  soon 
formed  around  the  zinc,  and  the  cell  is  ready  for  use. 

If  desired  for  immediate  use,  a  solution  of  zinc  sulphate 
may  be  prepared  and  poured  into  the  jar  with  the  copper 
sulphate  solution;  in  this  case  the  zinc  should  not  be  placed 
in  position  until  the  two  liquids  have  separated,  which  will 
be  indicated  by  the  upper  part  of  the  liquid  becoming  nearly 
colorless,  while  the  lower  part  is  of  a  deep  blue  color. 

2665.  The  average  internal  resistance  of  a  crowfoot 
cell  of  this  size  is  about  3  ohms,  and  its  E.  M.  F.  is  the  same 
as  the  other  forms  of  Daniell  cell,  1.07  volts. 

2666.  The  maintenance  of  this  type  of  cell  is  simple, 
it  only  being  necessary  to  renew  the  supply  of  copper  sul- 
phate crystals  when  the  solution  becomes  weak,  which  is 
indicated  by  the  fall  of  the  blue-colored  liquid  below  the  top 
of  the  copper  cathode;  besides  this,  the  density  of  the  zinc 
sulphate  solution  should  be  occasionally  measured  with  a 
hydrometer,  and  if  too  dense  (above  about  1.15  sp.  gr.)  a 
part  should  be  removed  and  replaced  by  water. 


BATTERIES. 


1737 


2667.  With  the  crowfoot  form  of  zinc  there  is  consid- 
erable waste,  due  to  the  size  of  the  **stub"  which  is  left 
when  the  zinc  has  been  consumed  so  that  it  can  not  be  used. 
Several  forms  of  zincs  have 
been  designed  to  prevent  this 
waste  as  far  as  possible. 

2668.  One  form,  used  by 
the  Baltimore  (Md.)  Fire  De- 
partment, is  cast  into  a  ring 
with  upwardly  projecting  lugs, 
which  have  shoulders  upon 
them,  by  which  the  zinc  is  sup- 
ported by  the  edge  of  the  bat-  fig.  1045. 

tery  jar.  This  form  of  zinc  is  illustrated  in  Fig.  1045.  The 
ring  itself  being  entirely  below  the  level  of  the  liquid  in  the 
cell,  it  can  be  almost  entirely  consumed. 

2669.  Fig.  1046  illustrates  another  similar  form,  known 
as  th.Q  pinnacle  zinc,  from  the  fact  that  it  is  supported  on  a 
vertical  rod  of  insulating 
material,  which  is  fast- 
ened at  the  lower  end  to 
the  copper.  This  rod 
projects  up  through  the 
liquids  and  enters  the 
cavity   in   the  center   of 


Fig.  1046.  Fig.  1047. 

the  brass  supporting  piece  B,  which  is  fastened  to  the  zinc  Z 
by  the  screws  S,  S.     The  complete  cell  is  shown  in  Fig.  1047, 


1738 


BATTERIES. 


Z  being  the  zinc,  C  the  copper,  and  P  the  rod  of  insulating 
material  which  supports  the  zinc  by  means  of  the  supporting 
piece  B. 

2670.     Another  form  of  zinc  in  which  there  is  no  waste 
whatever  is  the  D'Infreville  wasteless  zinc,  illustrated  in 


Fig.  1048. 

Fig.  1048.     This  zinc  is  cast  with  a  conical  lug  C  on  the  top, 
and  a  corresponding  cavity  in  the  under  side  of  the  zinc 

(see  Fig.  1049).  When  the  zinc  is 
nearly  consumed,  it  is  removed  from 
the  support  B^  and  the  lug  (7  inserted 
in  the  cavity  of  a  new  zinc,  which  is 
then  put  in  place  in  the  support  B. 
The  old  zinc  is  then  underneath,  and 
FIG.  1049.  is    entirely    consumed.       Fig.    1049 

shows  a  cross-section  of  this  form  of  zinc,  showing  a  new 
zinc  A,  a  partly  consumed  zinc  B,  and  the  stub  of  a  third  C. 
The  support  B  (Fig.  1048)  also  serves  as  a  connector,  the 
end  of  the  connecting  wire  being  sprung  in  between  the  two 
brass  strips  of  which  the  connector  is  made,  as  shown  at  W. 

2671.  The  Daniell  cell,  in  various  forms,  has  been  used 
as  a  standard  cell  in  laboratory  work  and  for  testing  pur- 
poses.  It  is  well  adapted  to  such  work,  if  too  great  a  degree 
of  accuracy  is  not  required,  as  the  E.  M.  F.  is  practically 
unaffected  by  moderate  changes  in  temperature  or  in  the  den- 


BATTERIES.  ItSQ 

sity  of  either  solution  used,  or  by  the  length  of  time  the  cell 
is  in  operation.  For  ordinary  work  the  E.  M.  F.  of  such  a 
standard  cell  may  be  taken  at  the  value  given;  that  is,  1.07 
volts.      (See  Art.  2655.) 


CELLS    WITH    A    SOLID    DEPOLARIZER. 

2672.  The  depolarizers  which  are  used  in  this  class  of 
cell  are  generally  substances  containing  a  large  proportion 
of  oxygen,  with  which  the  free  hydrogen  unites,  forming 
water;  the  balance  of  the  depolarizer  is  sometimes  dissolved 
in  this  water,  but  more  often  remains  at  the  cathode  in  a 
Bolid  form,  the  water  merely  serving  to  dilute  the  electro- 
lyte. In  the  first  case  the  solution  formed  usually  acts  to 
keep  up  the  strength  of  the  electrolyte.      (See  Art.  2597.) 

2673.  Some  few  of  the  non-metallic  elements  which 
exist  in  the  solid  state  will  unite  directly  with  hydrogen,  and 
might  be  used  as  depolarizing  cathodes;  such  a  substance  is 
the  metalloid  tellurhini.  Such  elements  are  rare  and  are 
not  used  in  commercial  forms  of  cells. 

^Q74r.  Among  the  most  widely  used  depolarizers  are 
the  oxides  of  manganese,  copper,  and  lead,  and  the  chlorides 
of  some  of  the  metals. 

The  several  sulphates  of  mercury  also  have  a  large  pro- 
portion of  oxygen,  and  are  used  for  this  purpose. 

2675.  The  Leclanche  cell  is  a  well-known  and  widely 
used  cell  of  this  type.  Its  positive  element  (negative  elec- 
trode) is  zinc,  usually  in  the  form  of  a  rod ;  the  electrolyte 
is  a  saturated  solution  of  ammonium  chloride,  NH JOI  (sal 
ammoniac),  and  the  negative  element  is  carbon,  surrounded 
by  manganic  oxide,  MnO^  (black  oxide,  or  peroxide,  of 
manganese),  which  is  the  depolarizer.  This  being  in  the 
form  of  a  coarse  powder,  it  is  usually  contained  in  a  porous 
cup,  which  allows  free  access  of  the  electrolyte  to  the 
depolarizer  and  negative  element. 

Fragments  of  crushed  coke  (or  carbon  in  other  forms)  are 


1740 


BATTERIES. 


often  mixed  with  the  manganic  oxide  to  decrease  the  resist- 
ance of  the  contents  of  the  porous  cup. 

Fig.  1050  shows  the  usual 
form  of  this  type  of  cell. 
The  porous  cup  P  contains 
the  manganic  oxide  and  the 
carbon  electrode,  which  pro- 
jects from  the  top  of  the 
cup,  and  to  which  a  binding- 
post  B  is  attached. 

The  glass  jar  is  circular, 
with  a  contracted  top,  in 
which  a  slight  recess  is 
formed  to  contain  the  zinc 
Z.  The  top  of  the  zinc  is 
provided  with  a  binding- 
screw  i?j,  which  serves  as 
the  negative  terminal  of 
the  cell,  B  being  the  posi- 
tive. 
FIG.  1050.  The    top    of    the   jar   is 

coated  with  parafHn  to  prevent  the  crystals  of  sal  ammoniac 
•'  creeping  "  over  the  top  of  the  jar  as  the  liquid  evaporates. 

2676.     The  cell  illustrated  in  Fig.  1050  is  of  the  follow- 
ing dimensions: 

Jar,  4|-  in.  diameter,  6    in.  high. 

Zinc,  f  in.  diameter,  6^  in.  high. 

Porous  cup,  3    in.  diameter,  h\  in.  high. 


Carbon, 


6  in.  X  If  in.  Y^^'wi.,  about. 


The  weight  of  the  zinc  rod  is  about  3  ounces,  about  two- 
thirds  of  which  is  below  the  level  of  the  liquid.  There  are 
about  16  ounces  of  peroxide  in  the  porous  cup,  and  it  re- 
quires nearly  6  ounces  of  ammonium  chloride  to  make  suf- 
ficient solution  for  this  size  of  cell. 

For  each  ounce  of  zinc  consumed  in  the  cell,  2  ounces  of 
manganic  oxide  and  2  ounces  of  ammonium  chloride  must 
also  be  consumed ;  so,  from  the  amount  of  these  materials 


BATTERIES.  1741 

contained  in  the  cell,  It  follows  that  there  is  enough  peroxide 
in  the  porous  cup  to  last  while  four  zincs  are  being  con- 
sumed, while  the  ammonium  chloride  will  not  last  longer 
than  1|-  zincs.  As  the  zincs  are  usually  replaced  when  eaten 
away  to  about  -J  in,  or  -^j-  in.  diameter,  the  solution  need  not 
be  replaced  until  two  zincs  have  been  consumed,  and  the 
contents  of  the  porous  cup  will  last  as  long  as  five  or  six 
zincs.  The  consumption  of  zinc  in  the  Leclanche  cell  is 
about  23  ampere-hours  per  ounce  of  zinc,  and  as  about  If 
ounces  of  each  zinc  rod  may  be  consumed,  the  life  of  each 
zinc  is  then  about  40  ampere-hours.  The  E.  M.  F.  of  this 
type  of  cell  is  about  1.48  volts,  and  its  internal  resistance 
about  4  ohms. 

2677.  It  is  usual  to  seal  the  carbon  and  depolarizer  into 
the  porous  cup  by  some  compound,  such  as  sealing-wax, 
leaving  small  tubes  or  holes,  by  which  whatever  gas  not  ab- 
sorbed by  the  depolarizer  may  escape.  This  sealing  neces- 
sitates the  entire  renewal  of  the  porous  cup,  with  contents, 
when  the  depolarizer  is  exhausted;  to  obviate  this  expense, 
some  makers  use  a  carbon  porous  cup  and  place  the  zinc  in- 
side, at  the  center,  the  space  between  the  zinc  and  carbon 
being  filled  with  peroxide. 

2678.  A  form  of  Leclanche  cell,  made  by  the  Law 
Battery  Co.,  also  replaces  the  clay  porous  cup  by  one  made 
of  carbon,  but  in  this  case  the  zinc  is  outside  the  carbon,  as 
in  the  regular  form.  The  carbon  cup  is  made  with  a  screw 
cover,  also  of  carbon,  which  renders  the  replacing  of  the  de- 
polarizer a  simple  matter.  This  construction  reduces  the 
cost  of  maintenance  of  the  cell,  but   increases  the  first  cost. 

2679.  Another  widely  used  form  of  Leclanche  cell  is 
the  Gonda  Leclanche,  which  uses  no  porous  cup  whatever; 
the  manganic  oxide  is  mixed  with  granulated  carbon  and 
some  gummy  substance,  and  compressed  into  cakes  under 
great  pressure.  These  cakes  are  attached  to  the  sides  of  the 
carbon  plate,  and  act  in  the  same  manner  as  the  depolarizer 
in  the  regular  form. 


1742 


BATTERIES. 


9 

o 

n 

I 

z 

J 

-< 

1 

i  '^i              1 

-3     '111 

C 

w 

G 

G 

i   ■'.              1 

i  M 

—J 

» 

) 

R 


Fig.  1051  shows  the  construction  of  the  elements  of  such 
a  cell.  The  two  cakes  of  depolarizer  (called  gondas)  G,  G 
are  clamped  one  on  each  side  of  the 
carbon  plate  C  by  the  soft  rubber  bands 
R,  R,  which  also  serve  to  hold  the  zinc 
rod  Z  in  place.  The  zinc  lies  in  a 
groove  in  a  block  of  wood  or  clay  W, 
which  serves  to  keep  the  zinc  away 
from  the  gondas.  This  block  is  some- 
times done  away  with  by  supporting 
both  zinc  and  carbon  from  a  plate  of 
insulating  material,  which  also  acts  as  a 
cover  to  the  jar.  In  still  other  forms, 
the  depolarizer  is  molded  into  a  cylin- 
^  der,  in  the  center  of  which  the  zinc  is 
supported. 

A    second     zinc     electrode     is     some- 
times used    in    this    latter  form,   consist- 
FiG.  1051.  ing  of  a  cylinder  of  sheet   zinc  encircling 

the  cylindrical  gonda,  a   common   terminal  being  connected 
to  both  zincs. 

The  liquids  and  action  of  the  gonda  form  are  the  same  as 
in  the  regular  Leclanche  cell. 

2680.  Commercial  sal  ammoniac  often  contains  a  con- 
siderable amount  of  impurities,  in  the  shape  of  other  salts, 
which  materially  reduce  the  life  of  the  electrolyte;  not  suf- 
ficiently, however,  to  warrant  the  cost  of  using  the  chemi- 
cally pure  salt,  as  prepared  by  chemists. 

2681.  Ammonium  chloride  has  been  found  to  be  the 
only  salt  which  works  well  with  manganic  oxide  as  a  de- 
polarizer, so  the  many  other  forms  of  cell  that  have  been 
constructed,  using  this  depolarizer,  differ  materially  from 
the  Leclanche  type  only  in  the  mechanical  arrangement  of 
the  parts. 

2682.  The  principal  chemical  actions  in  this  type  of 
cell  are  the  formation  of  zinc  chloride  and  ammonia,  and  the 
reduction  of  the  amount  of  oxygen  combined  with  the  man- 


BATTERIES. 


1743 


ganese.  Besides  these,  there  are  other  more  complicated 
reactions  which  occur,  but  which  do  not  affect  the  E.  M.  F. 
of  the  cell  materially. 


2683.  Another  solid  depolarizer  which  is  used  in  im- 
portant commercial  cells  is  cupric  oxide,  CuO.  The  La- 
lande  and  Chaperon  cell  uses  an  iron  or  copper  nega- 
tive element  surrounded  with  a  layer  of  cupric  oxide.  The 
positive  element  is  zinc,  the  electrolyte  a  solution  of  potas- 
siiiin  hydrate  (caustic  potash).  On  closing  the  external  cir- 
cuit, the  potassium  hydrate  solution  attacks  the  zinc,  form- 
ing a  compound  oxide  of  potassium  and  zinc,  known  ^.spotas- 
siuin  zincate,  and  liberating  hydrogen,  which  combines  with 
the  oxygen  of  the  cupric  oxide,  forming  water,  and  depositing 
metallic  copper  on  the  cathode. 

If  the  surface  of  a  solution  of  caustic  potash  is  exposed  to 
the  air,  it  will  gradually  form  potassium  carbonate;  to  pre- 
vent this  action,  cells  of  this 
type  are  either  entirely  en- 
closed or  the  surface  of  the 
liquid  is  covered  with  a  thin 
layer  of  heavy  oil. 

Fig.  1052  shows  one  form  of 
Lalande  and  Chaperon 
cell,  in  which  the  iron  vessel 
V  forms  the  negative  ele- 
ments, the  positive  terminal 
being  a  lug  A  cast  on  the 
side  of  the  vessel.  The  cupric 
oxide  B  is  in  a  layer  at  the  bot- 
tom of  the  vessel.  The  zinc  i? 
is  suspended  from  a  rod  K^ 
which  passes  through  a  rubber 
stopper  G,  terminating  in  a 
binding-post  F.  The  rubber 
stopper  is  provided  with  a 
valve  H,  which  allows  such 
gases  as  are  evolved  to  escape.  fig.  io58. 


1744 


BATTERIES. 


Several  other  forms,  of  greater  or  less  capacity,  are  man- 
ufactured. The  E.  M.  F.  of  this  type  of  cell  is  about  .7 
volt,  and  its  internal  resistance  is  usually  low. 

2684.  The  Edisoti-Lalande  cell  is  a  modification  of 
the  Lalande-Chaperon.  The  cupric  oxide  is  molded  under 
pressure  into  plates  of  the  requisite  size,  being  first  mixed 
with  magnesic  chloride,  which,  when  the  molded  plates  are 
heated,  serves  to  bind  the  mass  together.  These  plates  are 
held  in  copper  frames,  which  enclose  the  edges  of  the  plates. 
The  positive  element  in  this  cell  is  zinc,  and  the  electrolyte  a 
solution  of  potassium  hydrate,  as  in  the  Lalande-Chaperon 
cell.  Two  plates  of  zinc  are  used  in  most  of  the  forms  of 
this  cell,  one  on  each  side  of  the  cupric  oxide  plate. 

A  form  of  this  cell  is  shown  in  Fig.  1053,  which  repre- 
sents a  150-ampere-hour  cell.     The  cupric  oxide  plate  C  is 

suspended  in  a  cop- 
per frame  i%  F  be- 
tween the  two  zinc 
plates  Z,  Z,  which  are 
hung  from  each  side 
of  a  lug  on  the  por- 
celain cover  of  the 
jar.  The  sides  of  the 
copper  frame  of  the 
oxide  plate  are  car- 
ried up  through  the 
cover  supporting  the 
plate,  and  form  ter- 
minals B,  B,  either  of 
which  may  be  used 
as  the  positive  ter- 
minal of  the  cell. 
The  copper  frame  is 
protected  from  the 
action  of  the  liquid 
where  it  passes  up  through  by  tubes  of  insulating  material 
r,  T.  A  binding-post  B^,  on  the  bolt  which  supports  the 
two  zinc  plates,  serves  as  the  negative  terminal. 


Fig.  1053. 


BATTERIES.  1745 

A  heavy  paraffin  oil  is  used  in  this  cell  to  prevent  the 
action  of  the  air  on  the  solution ;  the  oil  layer  is  represented 
in  Fig.  1053. 

The  cell  shown  is  5^  in.  X  8^  in.,  outside  dimensions,  and 
will  give  a  current  of  3  amperes  at  a  potential  of  about  .7 
volt  for  50  hours,  which  is  equivalent  to  about  100  watt- 
hours,  with  one  "charge  "  of  zinc,  caustic  potash,  and  oxide. 

The  internal  resistance  of  the  above  cell  is  about  .07  ohm; 
the  weight  of  the  oxide  plate  is  about  ^  pound.  This  type 
of  cell  is  made  in  various  sizes,  ranging  from  a  15  ampere- 
hour  cell  for  telephone  and  similar  work,  to  900  ampere- 
hour  cells  for  running  lamps,  small  motors,  etc. 

2685.  There  are  several  oxides  of  lead  which  have 
been  used  as  depolarizers  in  single  liquid  cells:  plumbic  ox- 
ide, PbO,  known  as  litharge,  which  is  in  the  form  of  a  yel- 
lowish powder;  peroxide  of  lead,  PbO^,  and  a  combination 
of  the  oxide  and  the  peroxide,  Pb^O^,  known  as  minium, 
or  red  lead,  which  is  a  brilliant  red  powder. 

2686.  As  seen  from  its  formula,  the  peroxide  contains 
the  most  oxygen,  and  is  rather  the  best  depolarizer;  for 
example,  in  the  zinc,  dilute  sulphuric  acid,  and  carbon  cell, 
surrounding  the  carbon  with  lead  peroxide  increases  the 
E.  M.  F.  to  2.2  volts;  the  action  of  the  sulphuric  acid  on 
the  peroxide,  however,  forms  a  small  quantity  of  lead 
sulphate,  which  is  insoluble,  and  increases  the  internal 
resistance  of  the  cell  somewhat. 

Lead  peroxide  is  extensively  used  in  accumulators  (storage- 
batteries)  as  a  depolarizer. 

2687.  It  is  also  used  in  a  cell  (made  in  Europe)  which 
is  interesting  from  its  use  of  identical  electrodes;  that  is, 
both  anode  and  cathode  are  of  carbon,  arranged  as  follows: 
The  cathode  is  a  cylindrical  rod  of  carbon  surrounded  with 
lead  peroxide,  which  is  kept  in  place  by  a  canvas  bag.  The 
anode  is  a  perforated  carbon  cylinder,  made  to  slip  over  the 
cathode  and  its  surrounding  canvas.  The  whole  is  then  put 
in  a  glass  jar  and  surrounded  by  fragments  of  crushed  coke; 
the  jar  is  then  half  filled  with  a  strong  solution  of  sodium 


1746  BATTERIES. 

chloride.  The  lead  peroxide  is  reduced  to  lead  by  the  action 
of  the  hydrogen;  the  oxygen  (due  to  the  decomposition  of 
the  water)  combines  with  the  carbon  anode.  This  process 
goes  on  slowly,  so  that  if  much  current  be  drawn  from  the 
cell  it  will  polarize  by  the  formation  of  the  oxygen  on  the 
surface  of  the  anode. 

If  used  for  furnishing  feeble  currents,  this  cell  will  last  a 
long  time;  its  E.  M.  F.  is  about  .6  or  .7  volt. 

2688.  AH  cells  using  the  above-mentioned  solid  depo- 
larizers may  be  regenerated  by  passing  a  current  from 
some  other  source  through  them  in  the  opposite  direction 
to  that  of  their  own  current;  the  effect  of  such  a  current  is 
the  decomposition  of  the  various  substances  formed  by  the 
original  action  of  the  cell  and  their  recomposition  into  the 
original  substances  of  which  the  cell  was  composed.  If  the 
mechanical  construction  of  the  cells  is  such  that  these  sub- 
stances return  to  their  original  position  in  the  cell,  they  will 
again  act  as  a  voltaic  couple  from  which  a  current  may  be 
obtained. 

2689.  This  constitutes  a  storage,  or  secondary- 
battery,  or  accumulator. 

It  is  evident  that  such  a  cell  is  nothing  but  a  primary 
voltaic  cell,  which,  when  exhausted,  may  be  restored  by  the 
passage  through  it  of  a  current  from  an  external  source; 
there  is  no  real  storage  of  electricity,  so  the  name  storage- 
battery  is  hardly  correct;  the  last  name,  accumulator,  is 
more  appropriate  to  the  action  of  such  a  cell. 

Accumulators  will  be  treated  of  more  fully  later. 

2690e  The  principal  chlorides  used  as  depolarizing 
agents  are  the  chlorides  of  mercury  and  of  silver. 

If  the  carbon  of  a  zinc,  ammonium  chloride,  and  carbon 
cell  be  placed  in  a  porous  cup  and  surrounded  with  a  paste 
of  mercurous  chloride,  the  chemical  action  is  as  follows: 
The  ammonium  chloride  attacks  the  zinc,  forming  zinc 
chloride,  and  freeing  ammonia  and  hydrogen,  which  attack 
the  mercurous  chloride  and  reform  ammonium  chloride, 
leaving  free  mercury  at  the  negative  pole. 


BATTERIES.  1747 

The  ammonium  chloride  solution  is  thus  kept  up  at  its 
full  strength  until  the  mercurous  chloride  is  entirely  ex- 
hausted, and  the  hydrogen  is  recombined  as  fast  as  formed. 
Such  a  cell  has  an  E.  M.  F.  of  1.45  volts,  which  is  main- 
tained as  long  as  the  depolarizer  lasts,  if  excessive  currents 
are  not  used. 

2691.  The  chloride  of  silver  is  used  in  a  similar  man- 
ner. Cells  employing  this  depolarizer  use  as  a  negative 
element  a  silver  wire  or  plate  coated  with  silver  chloride. 
The  positive  element  is  usually  zinc,  and  the  electrolyte  a 
dilute  solution  of  one  of  the  chloride  salts. 

With  ammonium  chloride,  the  E.  M.  F.  is  1.03  volts; 
with  zinc  chloride,  1.02  volts,  and  with  sodium  chloride 
(common  salt),  0.97  volt. 

Silver  chloride  cells  are  quite  extensively  used  in  medical 
and  testing  work,  on  account  of  the  constancy  of  their 
E.  M,  F.  As  in  this  work  only  very  feeble  currents  are 
required,  this  type  of  cell  is  usually  made  small  and  of 
compact  form,  especially  as  the  use  of  the  silver  element 
would  make  a  large  cell  very  expensive.  The  chemical 
action  is  of  the  same  order  as  that  of  the  mercurous  chlo- 
ride cell  just  described;  that  is,  the  chlorine  part  of  the 
electrolyte  is  continually  replaced  from  the  depolarizer. 

2692.  The  various  sulphates  of  mercury  which  are 
used  as  depolarizers  are  the  mercuric  sulphate,  the  mer- 
curous sulphate,  and  a  sulphate  containing  a  still  higher 
percentage  of  mercury,  known  as  turbith  (or  turpeth)  min- 
eral. Either  sulphate  may  be  used  in  the  zinc,  dilute  sul- 
phuric acid,  and  carbon  cell  without  materially  affecting 
the  E.  M.  F.,  which,  under  these  circumstances,  is  1.3  to 
1.5  volts. 

These  sulphates,  being  slightly  soluble,  are  usually  em- 
ployed in  the  form  of  a  paste,  made  with  water  or  the 
exciting  liquid.  In  ordinary  work  the  mercury  sulphates 
are  not  extensively  used,  not  only  on  account  of  the  high 
cost  of  these  salts,  but  because  of  their  poisonous  qualities. 


1748  BATTERIES. 

Still,    these    sulphates    are    excellent  depolarizers,  and   are 
used  in  standard  cells. 

2693.  The  Latimer-Clark  cell,  in  which  the  electro- 
lyte is  a  paste  of  mercurous  sulphate,  formed  with  a  solution 
of  zinc  sulphate,  and  the  elements  are  zinc  and  pure  mer- 
cury, is  largely  used  as  a  standard  in  laboratory  work,  its 
E.  M.  F.  being  extremely  constant,  if  proper  precautions 
are  taken  in  its  construction.  With  chemically  pure  zinc 
and  mercury,  and  a  very  carefully  prepared  electrolyte,  the 
E.  M.  F.  of  a  standard  Clark  cell  at  15°  C.  is  1.434  volts. 
This  E.  M.  F.  varies  very  slightly  with  the  temperature,  the 
temperature  coefficient  being  .077^  per  degree  Centigrade, 
so  that  the  E.  M.  F.  at  any  temperature  may  be  expressed 
by  the  following  formula: 

Let  /  =  temperature    in    degrees    Centigrade    at    which 
measurement  is  made; 
E=-  electromotive  force  of  cell; 

then,  E  =  1.434  [1  -.00077  (/  ~  15)]  volts.  (472.) 

Thus,  for  example,  formula  472  gives  1.4507  volts  for 
this  cell  at  the  temperature  of  freezing  water,  0°  C,  and 
1.4155  volts  at  33°  C. 

The  greatest  accuracy  is  demanded  in  the  construction  of 
this  cell  and  in  the  determination  of  its  temperature  coef- 
ficient, because  the  cell  is  used  as  a  standard  in  the  measure- 
ment of  unknown  electromotive  forces. 

These  cells  are  used  as  standards  of  E.  M.  F.  only.  They 
do  not  supply  anything  but  very  minute  currents;  so  they 
are  made  of  conveniently  small  size,  and  the  most  approved 
forms  have  a  carbon  or  graphite  resistance  of  about  10,000 
ohms  connected  permanently  in  series  with  the  cell,  to  pre- 
vent its  accidental  short-circuiting  and  consequent  failure. 
These  cells  are  very  valuable  on  account  of  their  constancy, 
but  the  element  of  temperature  which  enters  in  makes 
them  somewhat  difficult  to  use  with  great  precision,  as 
thermometers  are,  as  a  rule,  inexact,  their  measurements 
depending  largely  on  their  physical  condition. 


BATTERIES. 


1749 


2694.  By  substituting  oxide  of  mercury  for  the  sul- 
phate, and  using  a  weak  (10^)  solution  of  zinc  sulphate  as 
the  electrolyte,  the  temperature  coefficient  is,  it  is  claimed, 
only  .01^  per  degree  C.  This  is  the  Gouy  standard  cell, 
which  has  an  E.  M.  F.  of  1.39  volts  at  12°  C. 


2695.  A  cell  has  been  designed  by  Mr.  Edward  Wes- 
ton, which,  it  is  claimed,  has  no  temperature  coefficient 
whatever  within  reasonable  limits.  This  cell  uses  for  the 
positive  element  the  metal  cadmium  in  the  form  of  an 
amalgam,  and  for  the  negative,  sulphate  of  mercury  mixed 
with  pure  mercury.  The  electrolyte  is  a  solution  of  some 
cadmium  salt,  preferably  the  sulphate.  The  E.  M.  F.  of 
this  form  of  cell  is  1.019  volts,  nearly.  The  mechanical 
construction  of  this  cell  makes  it  well  suited  for  general  use 
as  a  standard  cell,  it  being  entirely  sealed  into  and  enclosed 
by  a  solid  casing. 

The  cell  itself  is  similar  to  one  of  the  usual  forms  of 
standard  cells,  consisting  of  two  short  glass  tubes,  open  at 
the  end,  and  connected  together 
near  the  top  by  a  short  tube,  as 
represented  in  Fig.  1054,  in 
which  7",  T  are  the  two  tubes 
connected  together  by  the  short 
tube  S. 

In  the  bottom  of  the  tubes 
are  the  elements  P  and  tV,  to 
which  connection  is  made  by 
means  of  the  wires  W,  IV,  which 
are  sealed  into  the  glass.  These 
wires  are  led  to  binding-posts 
conveniently  mounted  on  the 
case.  The  space  above  the  ele- 
ments is  filled  with  the  electro- 
lyte, and  the  top  of  the  tubes  fig.  io54. 
fitted  with  corks  C,  C,  which  are  afterwards  sealed  in  place, 
preferably  with  some  resinous  compound.  The  elements, 
being  in  a  semi-liquid  condition,  are  each  kept  in  place  by  a 


1750  BATTERIES. 

piece  of  cloth  F,  with  a  perforated  cork  M  laid  over  it. 
When  this  is  forced  down  the  tube  to  the  surface  of  the 
element,  the  cloth  keeps  the  element  in  place,  and  the  cork 
holds  the  cloth,  the  perforations  allowing  free  access  of  the 
liquid  to  the  elements. 

This  is  the  general  form  in  which  most  standard  cells  are 
made,  although  the  various  makers  usually  introduce  slight 
changes  in  the  mechanical  construction, 

2696.  The  Bailie  and  Fery  cell  is  also  used  as  a 
standard  cell.  Its  action  is  similar  to  those  just  described, 
the  depolarizer  being  lead  chloride,  deposited  in  crystalline 
form  on  a  lead  cathode.  The  positive  element  is  amalga- 
mated zinc,  and  the  electrolyte  a  solution  of  zinc  chloride. 
The  E.  M.  F.  of  this  cell  is  .5  volt,  and  its  temperature  co- 
efficient is  low,  being  about  .02^  per  degree  C. 


CELLS  IN  ^¥HICH  AN  ELEMENTARY  SUBSTANCE 

IS  APPLIED  TO  THE  CATHODE  AS  A 

DEPOLARIZER. 

2697.  This  class  of  cells  is  not  large,  and  has  no 
extended  commercial  application,  at  least  in  this  country. 
The  principal  elements  used  for  depolarizers  are  those  com- 
prised in  that  group  known  as  halogens;  that  is,  chlorine, 
bromine,  iodine,  and  fluorine.  AlFthese  elements  will  com- 
bine with  hydrogen  directly,  forming  acids;  of  these  the 
formation  which  liberates  the  greatest  amount  of  energy  is 
that  of  hydrogen  and  chlorine  {HCl,  hydrochloric  acid); 
this  element  (chlorine),  therefore,  is  most  used  in  this  class 
of  cells,  as  it  results  in  a  high  E.  M.  F.  Chlorine  being 
normally  in  the  form  of  gas,  it  is  sometimes  generated  by 
chemical  action  in  suitable  apparatus  outside  the  cell,  and 
allowed  to  pass  through  the  cell  or  battery  of  cells  near  the 
cathodes,  acting  as  a  depolarizer  and  forming  hydrochloric 
acid. 

In  other  cases,  the  materials  whose  chemical  reactions 
produce  chlorine  are  brought  together  at  the  cathode,  and 
the  chloride  produced  acts  as  in  the  previous  method. 


BATTERIES.  1751 

As  a  rule,  some  or  all  of  the  other  products  of  the  chemi- 
cal actions  must  be  removed  as  fast  as  produced,  to  make 
room  for  a  fresh  supply  of  chemicals ;  in  any  case,  as  stated 
in  Art.  2606,  the  supply  of  depolarizing  element  is  inde- 
pendent of  the  output  of  the  cell,  and  must  be  regulated  by 
hand.  On  the  whole,  cells  of  this  class  would  be  expensive 
to  construct  and  maintain,  and  capable  only  of  limited  and 
special  application. 

2698.  Strictly  speaking,  cells  which  have  been  in- 
cluded in  the  class  given  in  Art.  2602,  whose  carbon 
cathode  is  made  of  large  surface  and  very  porous,  should  be 
included  in  this  class  (see  Art.  2617);  but  their  depolari- 
zation is  very  incomplete,  and  is  rather  accidental  than  a 
pronounced  feature  of  the  design;  hence,  they  are  placed 
in  the  former  class. 

DRY  BATTERIES. 

2699.  This  name  is  applied  to  cells,  usually  belonging 
to  the  class  mentioned  in  Art.  2605,  in  which  the  electro- 
lyte is  carried  in  the  pores  of*  some  absorbent  material,  or 
combined  with  some  gelatinous  substance,  so  that  the  cell 
may  be  placed  in  any  position  without  spilling  the  liquid. 

2700.  These  cells  are  usually  made  in  small  sizes,  with 
zinc  and  carbon  elements,  the  zinc  usually  forming  the  out- 
side of  the  cell,  being  made  into  a  sort  of  cylindrical  can,  in 
the  center  of  which  is  the  carbon,  surrounded  by  its  depo- 
larizing compound.  The  space  between  them  is  filled  with 
some  absorbent  material,  such  as  "mineral  wool,"  asbestos, 
sawdust,  blotting-paper,  etc.,  and  the  whole  is  then  soaked 
in  the  exciting  liquid ;  or  the  exciting  liquid  is  mixed  with  a 
hot  solution  of  some  gelatinous  body,  such  as  isinglass  or 
"Irish  moss,"  which  mixture  is  poured  into  the  cell;  on 
cooling,  it  forms  a  soft  jelly.  The  first  method  of  prepara- 
tion is  most  used. 

2701.  It  is  evident  that  only  a  comparatively  small 
amount  of  liquid  can  come  in  contact  with  the  zinc  at  one 


1752  BATTERIES. 

time,  so  the  current  output  must  be  small;  in  fact,  they  arc 
not  adapted  for  anything  but  intermittent  work.  It  is 
quite  necessary,  however,  that  they  have  a  depolarizer,  as 
otherwise  they  must  be  made  open  to  allow  the  hydrogen  to 
pass  off,  which  would  also  allow  the  small  amount  of  water 
they  contain  to  evaporate;  to  prevent  this  latter  action, 
these  cells  are  sealed  with  some  resinous  compound. 

2702.  Owing  to  the  presence  of  the  absorbent  material, 
the  actual  amount  of  liquid  in  these  cells  is  comparatively 
small;  consequently,  they  are  soon  exhausted.  The  sealing^ 
being  seldom  perfect,  often  allows  the  water  to  evaporate, 
in  which  case  the  cell  ceases  to  act;  a  cell  of  this  description 
may  often  be  made  to  work  when  apparently  exhausted  by 
drilling  a  small  hole  in  the  seal  and  injecting  a  little  water. 

2703.  The  materials  used  in  dry  batteries  are  usually 
kept  secret  by  their  manufacturers;  they  all,  however, 
answer  to  the  above  description  as  to  construction,  and  the 
best  types  employ  the  same  materials  as  the  Leclanche  bat- 
tery; that  is,  a  zinc  anode,  ammonium  chloride  electrolyte, 
manganic  oxide  depolarizer,  and  carbon  cathode. 

In  spite  of  its  defects,  this  form  of  cell  is  extremely  con- 
venient on  account  of  its  portability,  and  in  many  cases  can 
be  profitably  used. 

2704.  Silver  chloride  cells  (see  Art.  2691)  are  made 
in  a  sealed  form,  and  have  all  the  advantages  of  a  dry  bat- 
tery; the  materials  of  the  battery  are  enclosed  in  a  capsule 
of  semi-flexible  material,  which  allows  of  the  necessary  con- 
tractions and  expansions  of  the  apparatus.  In  this  form  these 
cells  are  very  convenient  for  testing  and  similar  purposes. 


THE  APPLICATION  OF  PRIMARY  BATTERIES. 
2705.  Although  the  cost  of  electricity  generated  by 
chemical  action  is  greater  than  that  generated  by  dynamo- 
electric  machinery,  there  are  many  cases  in  which,  from 
lack  of  motive  power,  or  from  the  small  amount  of  current 
required,  primary  batteries  may  be  successfully  used.     In 


BATTERIES.  1753 

such  cases,  the  cost  of  materials  consumed  in  producing  the 
electrical  energy  is  entirely  offset  by  the  little  attention 
required  and  the  constancy  of  the  source  of  supply;  and  in 
many  cases  where  current  is  used  intermittently,  the  cost  of 
the  current  from  a  battery  in  which  the  materials  are  con- 
sumed only  as  the  current  is  used  would  actually  be  less 
than  the  cost  of  the  power  for  driving  an  equivalent  dynamo 
all  the  time. 

2706.  The  most  important  applications  of  primary  bat- 
teries are  to  telegraph,  telephone,  and  electric  fire-alarm 
systems,  where  a  constant  but  small  current  is  required 
more  or  less  continuously,  although  in  large  central  offices, 
where  the  necessary  current  represents  a  considerable 
amount  of  energy,  dynamos  are  replacing  the  batteries  to 
some  extent,  on  account  of  the  saving  in  space.  For  this 
(telegraph,  telephone,  and  fire-alarm)  work,  gravity  batteries 
of  the  Daniell  type  are  more  commonly  used,  as  they  possess 
the  advantages  of  long  life  and  little  attention. 

2707.  For  telephone  work,  the  currents  used  are  very 
minute  indeed,  and  almost  any  good  cell  in  which  there  is 
no  local  action  and  in  which  the  depolarization  is  complete 
(at  least  for  small  currents)  will  give  good  results.  The 
E.  M.  F.  required  is  1.5  to  2  volts;  consequently,  in  some 
cases  single  cells  which  give  about  this  E.  M.  F.  may  be 
employed. 

2708.  In  fire-alarm  work  a  steady  current  of  (usually) 
.04  ampere  is  used,  the  potential  varying  with  the  length  of 
the  circuit.  Gravity  Daniell  cells  are  used  largely  in  this 
work,  the  zincs  being  made  large  and  heavy  to  insure  long 
life  and,  consequently,  little  attention. 

2709.  Several  systems  of  block  signaling  on  lines  of 
railroads  also  employ  electrical  devices  of  such  a  character 
that  gravity  Daniell  cells  are  well  suited  for  furnishing  the 
current  for  their  operation,  and  are  quite  extensively  used 
for  such  purposes. 


1754  BATTERIES. 

2710«  There  are  a  great  number  of  devices  which 
require  the  application  of  a  current  intermittently;  some, 
such  as  electric  bells  and  other  signals,  electric  gas-lighting 
apparatus  and  the  like,  are  used  infrequently  and  irregu- 
larly, and  the  amount  of  electricity  required  is  small,  so  that 
almost  any  voltaic  cell  will  do,  depolarizing  or  not,  provided 
there  is  no  local  action  to  cause  waste  when  not  in  use; 
therefore,  cells  with  liquid  depolarizers  (see  Art,  2604)  are 
not  well  adapted  to  this  work,  as  in  the  long  periods  in  which 
these  cells  are  not  called  upon  to  furnish  current  the  two 
liquids  will  mix  and  usually  cause  local  action. 

271 1.  The  cells  most  used  for  this  work  are  the  various 
zinc-carbon  batteries,  both  of  the  class  described  in  Art. 
2602,  with  non-depolarizing  electrolytes,  and  of  the  class 
described  in  Art.  2605,  with  solid  depolarizers;  of  the  lat- 
ter, some  form  of  Leclanche  cell  usually  gives  the  best  re- 
sults. In  hotels  and  large  buildings  where  the  bell  or  signal 
service  is  practically  continuous,  depolarizing  cells  are  re- 
quired, such  as  large  Leclanche  cells,  bichromates  (with 
separate  fluids),  if  of  good  modern  construction,  Edison- 
Lalande,  and  the  like. 

2712.  Electric  currents  are  much  used  in  physicians* 
and  surgeons'  offices;  currents  of  a  few  milliamperes  in 
strength,  but  of  from  75  to  100  volts  E.  M.  F.,  are  applied 
for  curative  purposes,  while  currents  of  10  to  20  amperes  in 
strength  are  used  for  heating  cautery  loops  in  surgical 
operations,  requiring  an  E,  M.  F.  of  from  4  to  8  volts. 
Miniature  incandescent  lamps,  usually  operated  from  the 
battery  which  furnishes  current  for  the  cautery,  are  also 
used  to  examine  the  interior  of  the  body. 

2713.  The  first  appliance  obviously  requires  a  large 
number  of  cells  of  a  small  size;  for  occasional  use,  and 
where  first  cost  is  not  such  an  object  as  compactness,  a 
battery  of  small  silver  chloride  cells  is  very  convenient, 
while  for  more  frequent  use,  requiring  larger  cells,  some 
cheaper  form  of  depolarizing  cell  is  used. 

Obviously,  if  the  cells  selected  have  a  high  E.  M.  F.  (say  2 
volts),  a  less  number  will  be  required  than  if  the  cells  are  of 


BATTERIES.  1755 

a  low  E.  M.  F.  ;  however,  as  in  some  instances  the  regula- 
tion of  the  current  is  obtained  by  switching  in  or  out  some 
of  the  cells,  this  regulation  will  be  more  uniform  and 
gradual  if  the  E.  M.  F.  of  each  cell  is  low. 

2714.  For  furnishing  the  larger  currents  for  cautery 
work,  large  cells  should  be  selected,  those  which  are  so 
arranged  as  to  have  a  minimum  internal  resistance  being 
best.  As  the  use  of  porous  cups  in  a  cell  increases  the  in- 
ternal resistance  largely,  cells  which  employ  them  are  not 
well  suited  for  this  work. 

Bichromate  cells  are  very  convenient  for  this  purpose,  as 
their  internal  resistance  is  low  and  the  E.  M.  F.  high  and 
steady.  It  is  usually  convenient  to  use  the  form  of  bi- 
chromate cell  in  which  the  elements  are  raised  from  the 
liquid  when  the  cell  is  not  in  use,  as  the  purpose  for  which 
the  current  is  used  involves  personal  and  immediate  atten- 
tion to  all  parts  of  the  apparatus. 

2715.  The  most  extensive  application  of  cells  of  the 
Bunsen  type  is  to  electroplating  and  similar  work,  and  cells 
of  large  size  are  made  especially  for  this  purpose. 

Such  work  being  usually  carried  on  in  establishments  es- 
pecially fitted  up  for  the  purpose,  the  various  unpleasant 
features  of  the  Bunsen  cell,  which  make  them  objectionable 
for  many  purposes,  may  be  readily  provided  for,  and  their 
high  and  constant  E.  M.  F.  utilized. 

2716.  The  minor  applications  of  primary  batteries  are 
almost  innumerable.  A  study  of  the  requirements  of  such 
cases  will  usually  determine  the  best  type  of  cell  to  use,  but 
attention  should  also  be  paid  to  the  mechanical  construction 
of  the  cells  selected,  as  on  this  point  often  depends  their  life 
and  suitability  for  the  work  they  are  called  upon  to  do. 

The  binding-posts  should  be  firmly  and  substantially  fixed 
to  the  elements,  and  should  be  thoroughly  protected  from 
possible  contact  with  the  electrolyte,  as  the  resulting  action 
will  so  corrode  the  joint  between  the  two  as  to  destroy  the 
contact,  besides  possibly  eating  away  the  connecting  wires 
and  breaking  the  circuit. 


1756  BATTERIES. 

Of  the  material  of  the  positive  element,  as  much  as  possi- 
ble should  be  below  the  level  of  the  liquid,  as  when  that  is 
consumed  the  balance  must  be  thrown  away,  and  this  may 
represent  a  considerable  loss. 

Altogether,  the  cell  should  be  substantial  and  compact, 
not  liable  to  local  action,  and  arranged  so  that  its  parts  may 
be  readily  renewed  with  the  least  possible  waste. 

2717.  In  general,  it  must  be  remembered  that  the 
consumption  of  material  in  a  primary  cell  (assuming  no 
local  action)  is  proportional  to  the  output  in  ampere-hours; 
the  energy  output  depends  not  only  on  the  amount  of  ma- 
terials consumed,  but  on  the  E.  M.  F.  of  the  cell  and  its 
internal  resistance,  so  that,  other  things  being  equal,  the 
higher  the  E.  M,  F.  of  a  cell  and  the  lower  its  internal 
resistance,  the  greater  its  output  for  a  given  cost  of 
materials. 

2718.  As  stated,  the  most  economical  metal  to  use  for 
the  positive  element  is  zinc,  and  the  amount  of  zinc  con- 
sumed in  a  cell  may  be  readily  determined  from  the  output 
in  ampere-hours  and  the  chemical  equivalent  of  zinc  (again 
assuming  no  local  action) ;  but  to  find  the  total  cost  of  the 
energy,  to  this  must  be  added  the  cost  of  the  depolarizer 
consumed,  if  any,  and  the  cost  of  labor  in  renewing  the  ma- 
terials and  caring  for  the  cells. 

2719.  The  substances  resulting  from  the  chemical  ac- 
tions which  take  place  often  have  a  market  value;  usually, 
however,  the  expense  of  collecting  or  preparing  such  sub- 
stances for  sale  will  be  greater  than  the  price  they  will 
bring,  so  that  in  ordinary  cases  this  should  not  be  taken  into 
account. 

2720.  It  is  evident  that  all  the  E.  M.  F.  of  a  cell  is  not 
available  to  send  a  current  through  the  external  circuit, 
but  that  a  part  is  expended  in  overcoming  the  internal  re- 
sistance. 

If  the  resistance  of  the  external  circuit  is  very  great,  this 
drop  is  of  little  importance;  while  if  the  external  resistance 


BATTJilRIES.  1757 

is  very  small,  the  internal  resistance  practically  determines 
the  amount  of  current  flowing. 

2>72>1.  The  various  methods  of  connecting  up  the  cells 
of  a  battery,  in  parallel,  series,  or  parallel  series,  are  given 
in  Art.  2250. 

If  several  cells,  all  of  the  same  size  and  kind,  are  con- 
nected in  series,  their  total  internal  resistance  will  equal 
^/le  resista7ice  of  one  cell  multiplied  by  the  miinber  of  cells,  and 
their  total  E.  M.  F.  will  equal  the  E.  M.  F.  of  one  cell  mul- 
tiplied by  the  number  of  cells ;  if  they  are  all  connected  in 
parallel,  their  total  resistance  will  be  equal  to  the  resistance 
of  one  cell  divided  by  the  number  of  cells,  while  their  total 
E.  M.  F.  will  be  equal  to  that  of  a  single  cell.  From  this  it 
follows  that  if  the  external  resistance  is  very  small,  increas- 
ing the  number  of  cells  in  series  will  not  increase  the  cur- 
rent in  the  external  circuit  appreciably,  as  the  resistance 
increases  nearly  as  fast  as  the  E.  M.  F. ;  while  if  the  exter- 
nal resistance  is  great,  increasing  the  number  of  cells  in 
parallel  will  not  appreciably  increase  the  current  flowing,  as 
the  total  resistance  is  not  much  altered,  while  the  E.  M.  F. 
remains  the  same. 

2722.  For  a  given  external  resistance  and  a  battery  of 
a  given  number  of  cells,  the  maximum  current  will  flow 
when  the  cells  are  so  grouped  that  their  internal  resistance 
just  equals  the  external;  so  that,  in  installing  a  battery,  the 
resistance  of  the  circuit  and  of  the  cells  should  be  ascer- 
tained, and  the   cells    grouped    accordingly.     This  may  be 

E 
proved,  numerically,  as  follows:   C  =  -^.     Let  m  cells  be  in 

series  in  /  rows,  or  a  total  of  m  X  /  cells.      Let  E  be  the 

electromotive  force  and  R  the  internal  resistance  of  each 

cell,    and    r  the  resistance  of  the  outside  circuit.     Substi- 

m  E 

tuting   in    above   formula,    C  =  -, ^ tt — ; —  id).     Then, 

{in  R  -\-  I)  -\-  r  ^  ' 

m  R 
C  is  greatest  when  — - — [-  r  is  smallest ;  that  is,  when  m  and 

/  are  chosen  such  that  -j-  R,  the  total  internal  resistance. 


I'^'SS  BATTERIES. 

equals  or  approximates  to  r.  Let  us  assume  m  x  I  ^=  12, 
^  =  2,  r  =  3,  i?  =  2.  Substituting  in  formula  (<«),  and  taking 
the  following  values  of  /, 

,      ,        ..  12  X  2  24  - 

^=1^      ^-(,o_X2)  +  3  =  24  +  3  =  -^""^P^^^- 

Total  internal  resistance  =  — =  24  ohms. 

J     ■         ^  6X2  12 

^-^-      ^=(|X2)  +  3  =  6T3^'-'""^P^^^^- 

Total  internal  resistance  =  6X2-^2  =  6  ohms. 
/      o       /-  4X2  8  ,  , 

Total  internal  resistance  =  4x2-4-3  =  2f  ohms. 
»./-.  oX2  6  _ 

Total  internal  resistance  =  3x2-4-4=  1|-  ohms. 

It  is  thus  seen  that  the  largest  current  is  obtained  when 
the  internal  resistance  approaches  nearest  to  the  value  of 
the  external. 

Ordinarily,  in  telephone,  telegraph,  and  fire-alarm  work 
the  external  resistance  is  high,  while  for  ringing  bells,  gas- 
lighting,  and  similar  work  the  resistance  is  low;  batteries 
for  these  purposes  should  be  grouped  accordingly. 

2723.  The  internal  resistance  of  a  cell  can  not  be 
measured  in  the  same  way  as  the  resistance  of  a  piece  of 
wire,  that  is,  by  sending  a  measured  current  through  it 
from  some  external  source,  measuring  the  drop  in  volts  and 
calculating  the  result  from  Ohm's  law ;  for  the  E.  M.  F.  of 
the  cell  itself  would  either  add  to  or  subtract  from  (depend- 
ing on  the  polarity  of  the  current)  the  drop  due  to  the  cur- 
rent, and,  hence,  the  calculated  results  would  be  at  fault. 

2724.  A  simple  way  to  measure  this  internal  resistance 
is  to  cause  the  cell  itself  to  furnish  a  current  through  some 
known  resistance.     Then,  by  measuring  the  E.  M.  F.  at  the 


BATTERIES.  1759 

terminals  of  the  cell  with  a  voltmeter,  when  the  current  is 
flowing  and  on  open-circuiting  the  cell,  the  difference 
between  the  two  readings  will  show  the  drop  in  volts  due  to 
the  flowing  of  this  current  against  the  internal  resistance  of 
the  cell. 

For  example,  if  a  cell  gives  an  E.  M.  F.  of  1.5  volts  on 
open  circuit,  and  on  being  connected  to  an  external  resist- 
ance of  2  ohms  the  E.  M.  F,  at  the  terminals  drop  to  1.25 
volts,  the  drop  in  the  cell  is  obviously  .25  volt.  The  cur- 
rent is  C  =  ^  =  ^^—  =  .625  ampere;  therefore,  the  internal 

resistance  of  the  cell  is  i^  =  -^  =  -^-— -  =  .4  ohm. 

C         .d2o 


ACCUMULATORS. 

27,25.  A  storage-battery,  or,  preferably,  an  accumu- 
lator, is  an  apparatus  consisting  of  certain  materials  so 
arranged  that  when  they  have  undergone  chemical  action, 
due  to  the  influence  of  a  current  of  electricity,  the  combina- 
tion has  acquired  the  properties  of  a  voltaic  cell,  and  is  en- 
abled to  discharge  into  a  closed  circuit  a  current  of  electricity 
approximately  the  same  as  the  original  charging  current. 

Many  forms  of  primary  batteries  may,  when  exhausted, 
be  more  or  less  regenerated  by  passing  through  them  a  cur- 
rent, from  some  external  source,  in  the  opposite  direction  to 
the  current  they  themselves  produce.  It  is  customary,  how- 
ever, to  consider  as  accumulators  only  those  cells  whose 
original  construction  is  similar  to  an  exhausted  battery; 
that  is,  they  can  not  be  used  as  sources  of  electricity  until 
they  have  been  cJiarged  by  passing  a  current  through  them. 

2726.     A  great  deal  of  confusion  exists  as  to  the  use  of 

the  terms  positive  and  negative  in  speaking  of  the  plates  of 
a  secondary  cell ;  for  in  charging  the  cell  the  current  is  in 
the  reverse  direction  to  that  which  flows  when  the  cell  is 
acting  as  a  voltaic  cell  and  discharging.  It  is  customary, 
however,  to  speak  of  the  plate  at  which  the  current  enters 
the  cell   (while   charging)   as  the  positive  plate.      In    fact, 


1760  BATTERIES. 

whether  charging  or  discharging,  his  plate  is  at  a  higher 
potential  than  the  other,  which  justifies  the  above  use  of  the 
term,  although  with  respect  to  the  chemical  actions  in  the 
cell  the  positive  and  the  negative  plates  are  reversed  in  the 
two  operations. 

2727.  Accumulators  may  be  divided  into  two  general 
classes  :    (1)    lead     accumulators,    and    (2)    bimetallic 

accumulators.     The  larger  proportion  of  cells  now  in  use 

are  of  the  first  class. 

2728.  Lead  Accumulators. — The  original  lead  ac- 
cumulators, as  made  by  Plante,  consist  of  two  plates  of  lead, 
usually  rolled  together  in  a  spiral,  and  separated  by  strips 
of  rubber  or  other  suitable  insulating  material;  these  are 
placed  in  dilute  (about  10^)  sulphuric  acid.  On  sending  a 
current  from  some  external  source  through  this  cell,  the 
water  becomes  decomposed,  and  the  oxygen  combines  with 
the  positive  plate,  forming  lead  oxide  or  peroxide,  while  the 
hydrogen  collects  at  the  negative  plate. 

On  disconnecting  the  source  of  the  applied  current,  and 
completing  the  external  circuit  of  the  cell,  the  water  again 
is  decomposed,  the  oxygen  uniting  with  the  hydrogen  col- 
lected at  the  negative  plate,  and  also  with  the  lead  plate 
itself,  and  the  hydrogen  uniting  with  the  oxygen  of  the 
oxide  of  lead  at  the  positive  plate,  thus  producing  a  current 
in  the  opposite  direction  to  the  applied  current. 

2729.  Owing  to  the  fact  that  the  formation  of  the 
layer  of  oxide  prevents  further  oxidation,  the  amount  of 
chemical  change  due  to  the  applied  current  is  small,  so  the 
secondary  current  from  the  cell  is  of  short  duration ;  after 
this  current  has  ceased,  however,  the  surface  of  the  positive 
plate  is  much  increased,  owing  to  the  removal  of  the  oxygen 
from  the  lead  oxide,  leaving  the  metallic  lead  in  a  spongy 
form.  On  again  sending  a  current  through  the  cell  a 
further  oxidation  of  this  (positive)  plate  takes  place,  and  by 
continuing  this  process,  reversing  the  current  each  time  it 
is  sent  through,  both  positive  and  negative  plates  become 
porous  to  a  considerable  depth,  thus  very  much  increasing 


BATTERIES.  1761 

the  surface  on  which  the  oxidation  can  take  place.  This 
process  might  be  carried  on  until  the  whole  plate  is  re- 
duced to  spongy  lead ;  in  that  case  the  plate  would  not  hold 
together,  so  a  sufficient  amount  of  the  original  plate  must 
be  left  for  mechanical  strength.  After  the  plates  are  so 
formed^  they  are  ready  to  be  used  as  an  accumulator. 

2730.  This  forming  process,  however,  is  too  long  and 
expensive  for  commercial  success,  though  it  is  considerably 
hastened  by  roughening  the  surface  of  the  lead  plates  with 
nitric  acid  before  commencing  the  process;  it  was  soon 
superseded  by  the  process  invented  by  Faure,  of  coating  the 
surface  of  the  plates  with  some  substance  which  by  the  first 
charging  current  is  converted  into  lead  peroxide  on  the  posi- 
tive plate  and  into  spongy  lead  on  the  negative.  This  sub- 
stance may  be  lead  oxide  (litharge),  lead  sulphate,  minium 
{Pb^O^),  lead  peroxide,  or  mixtures  of  these  substances. 

2731.  These  substances  are  applied  in  various  ways; 
one  method  is  to  make  a  paste  of  the  substance  (in  this  case 
usually  minium),  that  for  the  negative  plate  being  made 
with  sulphuric  acid,  which  changes  the  PbJD^  into  PbSO ^ 
(lead  sulphate)  and  water,  while  that  for  the  positive  plate 
is  made  with  water  only.  These  pastes  were  originally  ap- 
plied directly  to  the  surface  of  the  plain  lead  plate;  but  as 
they  proved  to  be  only  slightly  adhesive,  the  plates  were 
prepared  by  scratching  or  otherwise  roughening  the  surface, 
which  process  has  been  gradually  extended  until  the  lead 
plates  are  now  cast  into  grids,  or  latticework  plates,  in  the 
spaces  of  which  the  paste  is  applied,  or  forced  by  hydraulic 
pressure.  Some  manufacturers  do  not  use  a  paste  of  the 
active  material,  but  employ  the  minium,  litharge,  or  lead 
sulphate  in  the  form  of  dry  powder,  forcing  it  into  the  grid 
under  such  enormous  pressures  that  the  powder  is  solidified. 

2732.  The  grids  are  usually  designed  to  hold  the  active 
material  securely  in  position;  to  this  end  they  are  made 
with  perforations  which  are  not  of  the  same  area  through- 
out the  thickness  of  the  plate,  but  wider  or  narrower  in  the 


1763  BATTERIES.     ' 

center,  so  as  to  hold  the  filh'ng  of  active  material  by  the 
dovetailing  action  of  their  shape,  as  will  be  shown  later. 

•  2733.  After  the  grids  have  been  filled  with  active 
material,  they  are  set  up  in  pairs  in  suitable  vessels,  and 
surrounded  by  an  electrolyte  consisting  of  sulphuric  acid 
diluted  to  about  1.17  sp.  gr.,  which  density  corresponds  to 
about  20^  of  acid  in  the  liquid.  A  charging  current  is  then 
sent  through  the  cell  from  some  external  source ;  the  action 
of  this  current  decomposes  the  water,  the  oxygen  of  which 
further  oxidizes  the  lead  oxide  (litharge  or  minium)  to  per- 
oxide, at  the  positive  plate,  the  hydrogen  going  to  the  nega- 
tive plate,  where  it  reduces  the  lead  sulphate  to  spongy  lead 
by  uniting  with  the  SO^^  forming  sulphuric  acid.  Thus, 
the  active  material  becomes  lead  peroxide  in  the  positive 
plate  and  spongy  lead  in  the  negative.  By  many  investi- 
gators this  lead  peroxide  is  thought  to  be  Jiydrated  lead 
peroxide ;  that  is,  it  contains  a  certain  amount  of  hydrogen 
and  oxygen  in  excess  of  the  normal  peroxide,  and  is  repre- 
sented by  the  formula  H^Pb^O^.  This,  as  well  as  many  of 
the  actions  which  occur  in  accumulators,  is  not  clearly 
established  as  yet. 

2734.  Continuing  the  charging  current,  when  all  the 
active  material  is  thus  converted,  produces  no  further 
effect,  except  to  continue  to  decompose  the  water;  the  re- 
sulting gases  pass  off  through  the  water,  giving  it  a  milky 
appearance. 

This  phenomenon  is  known  as  gasing  or  boiling,  and  is  an 
indication  that  the  cells  are  fully  charged.  Continuing  the 
charging  current  beyond  this  point,  that  is,  overcharging 
the  cells,  does  no  harm  to  the  plates,  but  the  energy  repre- 
sented by  the  current  is  wasted. 

2735.  On  discontinuing  the  charging  current  at  the 
gasing  point,  and  completing  the  external  circuit  of  the  cell, 
a  current  will  flow  in  the  opposite  direction  to  that  of  the 
charging  current,  the  resulting  chemical  action  being  to 
reduce  the  lead  peroxide  to  lead  oxide  at  the  positive  plate, 
and  the  spongy  lead  to  lead  sulphate  at  the  negative;  a 


BATTERIES.  1763 

secondary  action  is  the  formation  of  a  part  of  the  lead  oxide 
at  the  positive  plate  into  lead  sulphate.  The  sulphates  thus 
formed  are  not  all  of  the  same  proportions;  one  exists  as 
red,  another  as  yellow,  and  a  third  as  white  crystals,  of 
which  the  white  sulphate  is  best  known,  as  it  is  formed 
when  the  cell  is  considerably  discharged,  and  is  extremely 
troublesome.  This  discharge  may  be  continued  until  all 
chemical  action  ceases,  and  the  E.  M.  F.  consequently  falls 
to  zero;  but  this  is  not  advisable,  since,  if  the  discharge  is 
carried  beyond  a  certain  point,  the  red  or  yellow  sulphates, 
probably  by  combination  With  the  litharge  {PbO),  form  the 
white  insoluble  sulphate,  which  has  a  higher  proportion  of 
lead  than  the  others;  this,  being  a  non-conductor,  materially 
increases  the  internal  resistance  of  the  cell,  and  when  it  is 
removed  it  usually  carries  some  of  the  active  material  with 
it,  as  it  is  very  adhesive. 

2736.  When  the  cells  have  been  properly  charged,  the 
positive  plate  is  of  a  brown  or  deep  red  color,  while  the 
negative  is  a  slaty  gray. 

The  presence  of  the  insoluble  sulphate  is  made  apparent  by 
the  formation  of  a  white  coating  or  glaze  over  the  plates,  which 
are  then  said  to  be  sulphated.  If  the  cells  are  discharged 
and  left  to  stand  with  the  electrolyte  in  place,  sulphating 
takes  place  rapidly. 

273T.  It  will  be  noticed  that  sulphuric  acid  is  formed 
during  thecharge,  and  decomposed  during  discharge ;  thus  the 
proportions  of  it  in  the  electrolyte,  consequently  the  density 
of  the  electrolyte,  vary  with  the  state  of  charge  of  the  cell; 
starting  with  a  specific  gravity  of  1.17,  when  the  cell  is  fully 
charged  the  specific  gravity  will  be  found  to  be  about  1.22, 
indicating  the  presence  of  about  25^  of  sulphuric  acid  in  the 
electrolyte. 

2738.  The  chemical  actions  of  charging  or  discharging 
do  not  take  place  simultaneously,  as  is  shown  by  the  varia- 
tions in  E.  M,  F.  under  different  conditions  of  charge  or 
discharge,  nor  are  they  probably  the  only  actions  which 
occur. 


1764  BATTERIES, 

2739.  The  E.  M.  F.  of  this  type  of  cell  is  approximately 
2  volts,  being  2.04  when  slightly  discharged,  which  gradually 
falls  to  1.90  volts  when  nearly  discharged.  Beyond  this 
point,  further  discharging  causes  the  E.  M.  F.  to  fall  more 
rapidly,  the  decrease  after  1.8  volts  being  very  rapid.  (See 
Fig.  1055.) 

2740.  The  rating  of  accumulators  is  usually  based  on 
their  capacity  when  discharged  to  an  E.  M.  F.  of  1.8  volts; 
but  in  spite  of  this  rating,  the  result  of  a  long  series  of  tests 
shows  that  in  practice  they  should  not  be  continuously  dis- 
charged to  below  1.9  volts,  as  below  this  point  sulphating  is 
very  liable  to  occur,  and,  the  nature  of  the  chemical  action 
being  changed,  it  also  leads  to  the  distortion  of  the  positive 
plate,  which  is  known  as  buckling. 

As  the  plates  are  located  very  close  together  in  the  cells 
to  reduce  the  internal  resistance,  buckling  is  liable  to  cause 
the  plates  to  touch,  thus  short-circuiting  the  cell. 

2741.  The  cause  of  buckling  seems  to  be  the  formation 
of  sulphate  in  the  plugs  of  active  material  which  fill  the 
spaces  of  the  grids,  thus  causing  the  plugs  to  expand;  lead 
having  very  little  elasticity,  the  grid  is  forced  out  of  shape. 
As  usually  constructed,  the  edges  of  the  grid  are  heavier 
than  the  intermediate  portion,  so  that  the  effect  of  the  dis- 
tortion is  to  bulge  the  plate  in  the  center.  If  the  plates  are 
not  discharged  too  far  and  too  rapidly,  the  expansion  of  the 
active  material  is  gradual,  causing  the  grid  to  stretch  evenly ; 
this  makes  the  plates  "  grow,"  or  increase  in  area,  sometimes 
as  much  as  10  per  cent. 

2742.  The  quantity  of  electricity  which  may  be  taken 
from  a  completely  charged  cell  depends  upon  the  amount 
(weight)  of  material  altered  by  the  chemical  action,  as  in  a 
primary  cell;  while  the  rate  at  which  this  material  is  altered, 
consequently  the  rate  at  which  the  electricity  can  be  taken 
out  (the  rate  of  discharge  in  amperes),  and,  to  a  large  extent, 
the  amount  of  material  altered,  depends  upon  the  surface  of 
the  active  material  exposed  to  the  chemical  action. 


BATTERIES. 


1765 


2743.  Cells  of  this  type  are  then  rated  at  a  certain 
number  of  ampere-hours  capacity,  depending  on  both  the 
weight  and  the  surface  area  of  the  active  material  in  the 
cell,  and  a  certain  economical  discharge  rate  is  also  recom- 
mended, depending  on  the  surface  of  the  plates  exposed  to 
the  electrolyte. 

If  this  discharge  rate  be  continually  exceeded,  the  chem- 
ical action  goes  on  too  rapidly,  the  white  sulphate  is  formed 
in  the  active  material  of  the  positive  plate,  finally  causing 
disintegration  of  the  active  material  and  buckling  of  the 
plates,  even  if  the  discharge  is  not  carried  beyond  the  point 
(1.9  volts  E.  M.  F.)  given  above.  With  the  ordinary  con- 
struction, the  normal  discharge  rate  is  about  .0165  ampere 
per  sq.  in.  of  surface  of  positive  plate,  and  the  discharge 
capacity  about  4.5  ampere-hours  per  pound  of  plate  (both 
positive  and  negative  plate  included). 

2744.  Fig.  1055  shows  the  manner  in  which  the  E.  M.  F. 
of  an  accumulator  falls  as  the  discharge  proceeds.     In  this 


L^ 

— 

— 

__^ 

-1, 

N 

\ 

~1, 

>^ 

I 

s. 

\ 

-1 

•cs 

-I 

KJ 

~1. 

Tl 

ME 

in 

TlOl 

JUS. 

1 

1 

i 

4 

t 

' 

( 

T 

12 

1 

FIG.  1055. 

case  the  cell  was  connected  to  a  variable  external  resistance, 
such  that  about  the  normal  discharge  current,  as  advised  by 
the  manufacturers,  was  maintained  throughout  the  test  in  the 


1766  BATTERIES. 

external  circuit.  The  oxidation  of  the  slight  layer  of  hydro- 
gen left  on  the  negative  plate  from  the  discharge  causes  the 
E.  M.  F.  to  be  high  at  first,  butas  this  is  quickly  disposed  of, 
the  E.  M.  F.  falls  in  the  first  ten  minutes  or  so  to  2.04  volts; 
on  continuing  the  discharge,  the  E.  M.  F.  falls  slowly  and 
evenly  until  after  about  8^  hours  of  discharging  the  E.  M.  F. 
falls  to  1.9  volts.  If  the  discharge  is  continued  beyond  this 
point,  the  nature  of  the  chemical  action  changes  somewhat, 
and  the  fall  of  E.  M.  F.  becomes  more  rapid,  at  10  hours 
being  1.8  volts,  and  at  11  hours  being  only  1.63  volts, 

2745.  This  falling  off  of  the   E.  M.  F.  is  due  to  the 

weakening  of  the  acid  solution  and  to  the  gradual  reduction 
of  all  the  spongy  lead  on  the  one  plate  and  the  peroxide  on 
the  other  to  sulphate. 

As  this  reduction  can  only  go  on  at  the  points  where  the 
acid  is  in  contact  with  the  spongy  lead  or  the  peroxide,  it  is 
evident  that  the  interior  portions  of  the  active  material  are 
affected  much  more  slowly  than  the  surface,  as  the  acid 
penetrates  the  active  material  only  at  a  comparatively  slow 
rate. 

On  this  account,  discharging  at  slow  rates  allows  the 
active  material  to  be  more  uniformly  and  thoroughly  re- 
duced, thus  giving  a  greater  output. 

This  also  accounts  for  the  fact  that  on  discontinuing  the 
discharge  at  any  point  the  E.  M.  F.  will  soon  rise  to  practi- 
cally its  original  value,  2.04  volts;  for  unless  the  cell  is 
entirely  discharged  there  is  always  some  unconverted  active 
material  in  the  interior  of  the  plate,  which  serves  to  give  the 
original  E.  M.  F.  when  reached  by  the  acid.  If  the  dis- 
charge is  resumed,  this  acid  is  soon  exhausted,  and  the 
E.  M,  F.  rapidly  falls  to  the  value  it  had  when  the  discharge 
was  stopped. 

2746.  In  the  above  case,  the  product  of  the  amperes 
and  the  hours  will  give  the  output  of  the  accumulator  in 
ampere-hours;  if  the  discharge  rate  had  been  greater,  the 
output  in  ampere-hours  would  have  been  diminished,  the 
discharge  being  continued  until  the  E.   M.   F.  falls  to  the 


BATTERIES.  1767 

same  value  In  each  case.  Conversely,  if  the  discharge  rate 
had  been  lower,  the  output  would  have  been  increased. 

For  example,  assume  the  limiting  E.  M.  F.  to  be  1.9  volts. 
In  a  certain  cell,  with  a  discharge  current  of  30  amperes, 
the  E.  M.  F.  reaches  its  limit  in  10  hours,  giving  an  output 
of  300  ampere-hours. 

If  the  discharge  current  were  40  amperes,  the  limiting 
E.  M.  F.  would  be  reached  in  about  6|-  hours,  giving  an  out- 
put of  only  260  ampere-hours;  while  if  it  were  20  amperes, 
the  limiting  E.  M.  F.  would  not  be  reached  for  about  17i 
hours,  giving  an  output  of  350  ampere-hours. 

For  the  sake  of  uniformity,  the  rating  of  the  capacity  of 
accumulators  is  made  on  the  basis  of  a  discharge  current 
which  will  cause  the  E.  M.  F.  to  fall  to  1.8  volts  in  10  hours, 
although  most  manufacturers  give  tables  showing  the  com- 
parative capacity  of  the  various  sizes  of  cells  at  other  rates 
of  discharge. 

2747.  The  rate  of  charge  (charging  current)  for  accu- 
mulators of  this  class  should  be  about  the  same  as  the  nor- 
mal (10-hour)  discharge  rate,  although  much  smaller  cur- 
rents, continued  for  a  proportionately  longer  time,  may  be 
used. 

2748.  Although  "storage-batteries  "  do  not  store  elec- 
tricity, they  certainly  do  store  energy  by  converting  the 
kinetic  energy  of  the  electric  current  into  chemical  potential 
energy,  which  may  be  realized  as  kinetic  energy  again.  The 
efficiency  of  the  accumulator  (or  of  any  other  means  of  stor- 
ing or  transforming  energy)  is  the  output  divided  by  the 
input.  This  quotient  is  always  less  than  1,  as  the  accumu- 
lator is  not  a  perfect  storer  of  energy ;  that  is,  there  are 
certain  losses  in  the  transformation  of  kinetic  electrical  to 
potential  chemical  energy,  and  vice  versa,  besides  the  loss  of 
the  energy  required  to  force  the  current  through  the  cell, 
that  is,  the  loss  due  to  the  resistance  of  the  plates  and  elec- 
trolyte. 

2749.  The  input  and  output  of  an  accumulator  may 
be    expressed    either    in    ampere-hours    (the    quantity    of 


1768  BATTERIES. 

electricity)  or  in  watts  (the  rate  of  doing  zuork  of  the  cur- 
rent). If  secondary  cells  of  this  class  be  fully  charged  at 
normal  rate,  after  a  discharge  to  1.8  volts,  and  then  dis- 
charged to  the  same  point,  also  at  normal  rate,  the  ampere- 
hour  efficiency  will  be  ordinarily  from  .87  to  .93,  or  87^  to 
93^.  If  charged  and  discharged  to  the  same  point  at  very 
slow  rates,  this  efficiency  may  rise  to  96^  or  97^. 

2750.  The  watt  efficiency  at  normal  rates  of  charge  and 
discharge  is  lower,  being  from  65^  to  80^,  depending  on  the 
construction  of  the  cell.  In  larger  cells  of  modern  con- 
struction, the  watt  efficiency  is  as  high  as  84^. 

2751.  The  cause  of  the  loss  represented  by  the  fore- 
going figures  is,  for  the  ampere-hour  efficiency,  due  to  the 
fact  that  the  charging  current  must  perform  several  chemi- 
cal decompositions,  of  which  the  elements  either  do  not 
recombine  in  the  cell  or,  recombining,  do  not  give  up  their 
potential  energy  in  the  form  of  electrical  energy.  This  loss 
varies  with  the  rate  of  charge  and  discharge,  as  indicated 
by  the  figures  given,  but  for  a  given  rate  it  is  practically 
fixed,  the  mechanical  arrangement  of  the  cells  having  little 
effect  upon  it. 

2752.  The  greater  loss  shown  in  the  watt  efficiency 
figures  is  due  to  the  fact  that  the  E.  M.  F.  of  charge  is 
higher  than  that  of  discharge,  due  in  part  to  the  E.  M.  F. 
required  to  perform  the  wasteful  chemical  actions  referred 
to  above,  but  largely  to  the  drop  in  volts  caused  by  the 
passage  of  the  current  against  the  resistance  of  the  plates 
and  electrolyte.  This  drop  adds  to  the  E.  M.  F.  required  to 
perform  the  chemical  decomposition  in  charging,  and  sub- 
tracts from  the  E.  M.  F.  due  to  the  chemical  recompositions, 
and  its  amount  depends  more  on  the.  construction  of  the 
cell  than  does  the  loss  represented  by  the  ampere-hour  effi- 
ciency, as  it  varies  with  the  shape  and  size  of  the  plates, 
their  distance  apart,  their  state  of  charge  (on  account  of 
variations  of  the  resistance  of  the  electrolyte  as  the  percent- 
age of  acid  varies)  and  other  conditions. 

This  loss  due  to  the  internal  resistance  in  well-designed 


BATTERIES. 


1769 


cells  usually  amounts  to  about  8^,  at  normal  rates  of  charge 
and  discharge ;  the  loss  is  correspondingly  less  at  low  rates 
and  more  at  high  rates,  being  proportional  to  the  square  of 
the  current  flowing. 

In  a  good  modern  cell  exposing  about  1,100  sq.  in.  of 
positive  plate  surface,  the  internal  resistance  is  about  .005 
ohm  when  charged.  Cells  of  greater  capacity  than  the 
above  (which  is  listed  as  350  ampere-hours)  would  have  a 
proportionately  lower  resistance. 

2753.  The  above  efficiency  figures,  as  stated,  are  given 
for  a  discharge  to  1.8  volts  E.  M.  F.,  the  usual  manufac- 
turers' rating;  if  the  cells  are  not  discharged  to  so  great  an 
extent,  both  ampere-hour  and  watt  efficiencies  are  higher. 

2754.  The  E.  M.  F.  required  to  send  a  given  charging 
current  through  a  secondary  cell  varies  with  the  state  of 


—2 

Cr, 

^_ 

- 

pi 

/ 

/ 

•<:* 

■2-^ 
^ 

y 

, 

^ 

^ 

r 

1 

0 

T. 

rjsIE 

i,n 

HO 

URS 

a  I 

{ 

* 

i 

'. 

I 

1 

" 

1 

r 

Fig.  1056. 
charge  of  the  cell.     Fig.  1056  shows  the  E.  M.  F.  required 
to  charge  the  same  cell  that  gave  the  discharge  E.  M.  F. 
curve  (Fig.  1055),  being  in  this  case  charged  at  the  same 
rate  as  previously  discharged. 

This  curve  shows  that  the  charging  E.  M.  F.,  after  a 
quick  rise  in  the  first  few  minutes  to  about  2.06  volts, 
gradually  rises  during  the  first  6  or  7  hours,  after  which  the 
rise  is  more  rapid,  until  after  11  hours  of  charging  it  becomes 


1770  BATTERIES. 

2.5  volts;  at  this  point  gasing  begins  and  the  cell  is  practi- 
cally charged.  On  continuing  the  charging  current,  the 
E.  M.  F.  rises  a  little  more,  and  then  remains  practically 
constant  at  about  2.55  volts;  as  the  only  action  which  now 
takes  place  is  the  decomposition  of  the  electrolyte,  giving 
ofif  gas,  further  charging  would  only  result  in  a  waste  of 
energy;  although  long-continued  overcharging  at  a  mod- 
erate rate  will  gradually  remove  any  formations  of  white 
sulphate  that  may  exist.     (See  Arts.  2734  and  2736.) 

2755.  From  this  curve  it  appears  that  the  cell  became 
completely  charged  in  practically  11  hours;  as  the  discharge 
curve  (Fig.  1055)  shows  that  with  the  same  number  of 
amperes  the  discharge  is  complete  (to  1.8  volts)  in  10  hours, 
the  ampere-hour  efficiency  of  this  cell  is  W^  or  91^,  prac- 
tically. 

2756.  If  an  accumulator  of  this  class  is  not  discharged 
at  an  excessive  rate  nor  to  more  than  1.9  volts  E.  M.  F.,  the 
positive  plates  should  last  for  about  1,200  or  more  dis- 
charges; while  if  discharged  each  time  to  below  1.8  volts, 
or  at  excessive  rates,  the  life  of  the  positive  plate  will  not 
ordinarily  be  more  than  400  or  500  discharges.  The  nega- 
tive plates,  with  good  care,  will  usually  outlast  four  or  five 
positive  plates. 

Some  of  the  more  modern  cells  of  this  class  will  show 
better  results  than  the  above,  which,  however,  are  good 
average  figures. 

2757.  The  usual  construction  of  cells  of  this  class  is  as 
follows : 

The  plates  and  electrolyte  are  contained  in  a  vessel  of 
approximately  cubical  form;  this  vessel  is  of  glass,  if  the 
cells  are  not  intended  to  be  portable,  the  glass  allowing 
the  examination  of  the  condition  of  the  plates  while  the  cell 
is  in  operation.  If  the  cells  are  intended  to  be  portable, 
the  vessel  is  usually  made  of  hard  rubber  or  gutta-percha,  ot 
of  wood  lined  with  hard  rubber  or  lead.  Very  large  accu- 
mulators for  central-station  use  are  usually  set  up  in  lead- 
lined  wooden  tanks. 


BATTERIES. 


1771 


2758.  The  plates  are  usually  approximately  square,  and 
from  ^  inch  to  ^  inch  thick,  according  to  size.  To  get  a 
large  surface  area  without  using  single  large  plates,  and  to 
allow  of  one  size  of  plate  being  used  for  cells  of  various 
capacities,  each  cell  contains  a  number  of  positive  and  nega- 
tive plates,  arranged  alternately  side  by  side  a  short  distance 
apart.  The  number  of  negative  plates  is  always  one  more 
than  the  number  of  positive  plates,  so  that  eac/i  side  of  each 
positive  plate  has  presented  ^ 

to  it  the  surface  of  a  nega-  'nX 
tive.  All  the  positive  plates 
are  connected  together  by  a  y- 
connecting  strip,  usually  at 
one  corner  of  the  plate,  and  ^' 
all  the  negatives  are  similarly  y. 
connected.  The  arrangement 
of  a  typical  accumulator  cell  ^' 
is  represented  in  Fig.  1057,  ^v- 
where  N,  N,  N,  N,  N  are  the 
negative  plates  and  P,  P,  jP,  P 
the  positive.  From  a  corner 
of  each  plate  a  lug  projects; 
the  lugs  on  the  negative 
plates  are  joined  to  a  con- 
necting strip,  as  represented 
at  T,  and  the  lugs  on  the 
positive  plates  are  similarly 
joined  to  a  connecting  strip 
T'.  The  joints  are  made 
by  a  process  called  "burn- 
ing," which  consists  in  melt- 
ing the  lugs  and  strip  together  by  a  flame  of  hydrogen. 
This  hydrogen  flame  absorbs  the  oxygen  from  the  film  of 
lead  oxide  with  which  the  lead  is  usually  covered,  thus 
making  a  clean  and  solid  joint.  These  connecting  strips 
are  extended  beyond  the  limits  of  the  cell,  and  serve  to 
connect  the  various  cells  of  the  battery  together,  as  shown 
at  C,  the  connection  being  made  by  a  brass  bolt,  which 
clamps  the  connecting  strips  together  firmly. 


1773 


BATTERIES. 


2759.  The  plates  are  placed  in  the  jary,  resting  on  a 
wooden  support  made  from  two  strips  of  wood  (usually 
boiled  in  paraffin)  of  triangular  section  S,  S.  These  support 
the  plates  at  such  a  height  that  any  loosened  particles  of 
active  material  fall  below  the  level  of  the  bottom  of  the 
plates,  thus  preventing  possible  short-circuiting.  When  in 
position,  the  electrolyte  is  poured  in  until  it  reaches  the 
line  L  L,  thus  covering  the  plates.  To  prevent  the  plates 
from  touching  each  other,  it  is  usually  the  practice  to  sepa- 
rate them  by  blocks  or  strips  of  insulating  material,  the 
exact  arrangement  varying  with  the  different  manufac- 
turers. 

2760.  Owing  to  the  expense  oi  forming  t\\.Q.  plates  by  the 
Plante  process,  cells  of  the  construction  invented  by  Faure, 
known  as  "pasted  plate"  cells,  have  been  very  extensively 
used.  Those  principally  used  abroad  are  known  as  the 
Faiti'e-Sellon-Volkmar  cells,  from  the  company  owning  the 
principal  French  patents. 

2761.  Sections  of  the  grids  principally  used  by  this 
company  are  shown  in  Figs.  1058  and  1059.  The  first  is 
cast  of  lead  alloyed  with   a  little  antimony  to  give  stiffness 


EHcdn 

nnmn 
nnmn 
nnnn 


Fig   1058. 


Fig.  1059. 


to  the  grid,  and  oxide  paste  is  forced  into  the  openings  in 
the  grid  {n^  n,  n).  The  section,  taken  at  the  line  a  b^  shows 
the  shape  of  these  openings. 


BATTERIES. 


1773 


2762.  The  second  grid  is  made  of  two  plates  cast  sepa- 
rately and  afterwards  riveted  together  with  lead  rivets.  In 
this  grid,  as  shown  by  the  section,  the  openings  for  the 
paste  (;z,  it,  n)  are  larger  in  the  center  of  the  plates  than  at 
the  faces,  thus  securely  holding  the  plugs  of  active  materials. 

2763.  Grids  similar  to  those  shown  in  Fig.  1057  are 
used  in  the  E.  P.  S.  accumulator  in  England  and  in  the 
cells  made  by  the  Electric  Accumulator  Co.,  the  Julien  Co., 
in  the  United  States,  and   by  other  manufacturers. 

2764.  In  Germany,  where  the  accumulator  has  been 
most  extensively  employed,  more  complicated  forms  of  grids 
are  used.     One  of  these  is  shown  in  Fig.  1060;  it  consists  of 


Fig.  1060. 

a  double  lattice  united  at  the  edges  of  the  plate,  and  kept  at 
a  little  distance  apart,  as  shown  in  the  section,  by  small 
columns  at  the  points  where  the  members  of  the  two  lattices 
cross,  as  represented  at  c  c.  This  plate  is  cast  at  one 
operation.  This  form  of  plate  holds  a  large  quantity  of 
active  material,  and  is  quite  stiff.  Even  more  complicated, 
grids  are  used,  some  consisting  of  three  layers  of  lattice- 
work, separated   by  columns, 'as  in  the  grid  just  described. 

2765.  Fig.  1061  represents  a  section  of  the  Tudor 
grid,  a  form  of  pasted-plate  grid  which  has  many  good 
features;  it  is  composed  of  a  number  of  small  square  or 
rectangular  grooved  grids  G^  about  6   inches  square,  with 


1774 


BATTERIES. 


the  active  material  pasted  or  forced  in  the  grooves  as  in 
the  ordinary  form  (see  section,  Fig.  1061).  Six  or  more  of 
these  small  grids  are  then  fastened  by  a  lug  on  one  edge,  as 
at  C,  to  the  bars  of  a  cast  lead  supporting  frame  i%  which 
has  openings  between  the  bars  slightly  larger  than  the  small 
grids  which  they  enclose.  The  small  grids  are  thus  free  to 
expand  or  contract  without  interfering  with  the  plate  as  a 
whole,  thus  preventing  to  a  large  extent  buckling  and  dis- 
integrating of  the  plate,  and  any  damaged  grid  may  be 
replaced  without  disturbing  those  remaining. 

3766.  Accumulators  employing  this  form  of  grid  are 
largely  used  in  central  stations  in  Germany,  and  also  form 
one  of  the  largest  accumulator  installations  in  the  United 
States,  that  of  the  Edison  Electric  Illuminating  Co.,  of 
Boston,  Mass.,  which  consists  of  two  sets  of  70  cells  each, 
each  set  having  a  capacity  of  about  3,500  ampere-hours. 
Other  forms  of  grids  are  also  made  by  the  same  company, 
and  are  also  known  as  Tudor  grids. 

2767.  Fig.  1062  illustrates  the  grid  used  in  the  Sor- 
ley  cell,  made  in  the  United  States.     It  is  made  of  strips 

_n  n    »  §   _   _  of  lead  s,  s,  s  of  uniform  width  and 

thickness,  which  are  bent  into  the 
shapes  shown,  and  are  held  in  place 
by  other  strips  around  the  edge  of 
the  plate.  These  strips  are  led  out 
at  the  upper  edge  to  form  a  termi- 
nal. The  oxide  paste  is  forced  into 
the  openings  between  the  strips  at 
n,  jz,  7i,  as  in  the  cast  grids.  The 
advantage  claimed    for  this  type  of 

grid  is  that  it  allows  of  free   contraction   and  expansion  of 

the  active  material. 

2768.  A  form  of  grid  which  is  cast  around  the  plugs 
of  active  material  is  represented  in  Fig.  1063.  This  grid 
was  invented  by  Reckenzaun  for  use  in  street-car  propul- 
sion; the  active  material  is  prepared  in  cylindrical  plugs, 


Fig.  1062. 


BATTERIES. 


1775 


r  /        

\    l----^ 

-rr:^ 

1 

J        1 

1 

---\    f— - - 

I 

.  ...]    I 

^ 

-  -  -1    1    - -- 

i 

—J     1—- 

( 

1     1 *T^ 

r  ' 

\ 

\    t H' 

V 

y' 

i 

!t 

Fig.  1063. 


shown  at  c,  which  are  laid  in  a  corrugated  mold,  and  the 
melted  lead  alloy  poured  in  around  them.  They  are  thus 
held  quite  firmly  in  place,  ^ 

while  exposing  a  considera- 
ble surface  to  the  electro-      ^^^=,^^^    ^^^^,,,^,^^3^ 

lyte.  "  As  can  be  seen  from      |„. Itttzi    \ - 1  Q 

the  section,  taken  along  the      i i-Tzn    i-  J  t  . 

line  a  b^  the  cylindrical  form 
of  the  plugs  holds  them  in 
place,  even  if  the  plate  be 
bent  considerably. 

2769.  None    of     the 
pasted-plate  cells,  however, 
is  as  substantial  as  those  in  which  the  active  material  is 
formed  from  the  plate  itself,  as  in  the  Plante  cell. 

The  principal  objection  to  the  Plante  process  being  the 
length  of  time  required  to  alter  the  surface  of  the  plates 
from  a  smooth  to  a  spongy  condition,  attempts  have  been 
made  to  construct  plates  which  are  porous  at  the  start,  such 
as  compressing  lead  dust,  or  fine  threads  of  lead  made  by 
blowing  a  stream  of  air  through  melted  lead,  etc.,  deeply 
grooving  or  even  slitting  the  plates  to  increase  the  surface; 
none  of  these  processes  has  resulted  in  a  plate  which  is 
substantial  enough  for  commercial  use. 

2770.  A  form  of  cell  in  which  it  is  claimed  the  plates 
combine  the  cheapness  of  preparation  of  the  pasted  plate 
with  the  greater  solidity  and  longer  life  of  the  Plante  plate 
is  the  chloride  accumulator  made  in  this  country  by  the 
Electric  Storage  Battery  Co.,  of  Philadelphia. 

2771.  The  plates  of  this  type  of  cell  are  made  as  fol- 
lows: A  mixture  of  zinc  chloride  and  lead  chloride  is  melted 
and  run  into  molds,  which  form  it  into  cylindrical  pellets 
or  pastilles,  which  have  a  bevel  /\  shaped  edge,  being 
thus  larger  in  the  center  than  at  the  faces.  These  pellets 
are  placed  in  a  second  mold,  being  held  in  position  by  steel 
pins,  and  an  alloy  of  lead  and  antimony  is  melted  and  forced 
in  between  the  pellets  under  heavy  pressure.     When  this 


1776 


BATTERIES. 


cools  it  forms  a  plate,  binding   all   the  pellets  of  zinc  and 
lead  chloride  together. 

2772.  This  plate  can  not  be  used  in  this  form  in  an 
accumulator;  a  number  of  these  are  first  set  up  in  a  bath  of 
dilute  zinc  chloride  with  plates  of  zinc,  to  which  the  lead 
plates  are  connected.  These  plates  then  act  as  the  elements 
of  a  primary  battery,  and  the  resulting  chemical  action  dis- 
solves out  the  zinc  chloride  from  the  pellets,  and  converts 
the  lead  chloride  into  metallic  lead,  which  assumes  a  crystal- 
line form.  The  plate  is  now  practically  a  continuous  lead 
plate,  solid  and  dense  in  some  parts  and  porous  in  others. 

2773.  The  plates  in  this  condition  are  suitable  for 
negative  plates;  those  required  for  positive  plates  are  then 
set  up  with  plain  lead  plates  in  a  bath  of  dilute  sulphuric 
acid,  and  a  forming  current  sent  through  them  from  the 
prepared  plates  to  the  plain. 

This  current  causes  the  porous  parts  of  the  plates  to  be 

formed  into  lead  peroxide  and 
sulphate ;  the  plate  is  now  the 
equivalent  of  a  pasted  plate, 
and  is  an  improvement  through 
having  its  active  material  firmly 
bound  in  place  in  the  com- 
pressed grid.  Fig,  1064  shows 
a  part  of  one  of  these  plates; 
the  section,  taken  along  the 
^  line  a  b,    shows   the    shape    of 

Fig.  1064.  these  plugs.     The  holes  in  the 

plugs  are  caused  by  the  pins  by  which  they  are  supported 
in  the  mold. 


2774.  The  requisite  number  of  these  prepared  plates 
are  then  set  up  together  to  form  a  cell,  alternate  positives 
and  negatives  being  connected  to  common  conductors,  as  in 
other  types  of  cells.      (See  Fig.  1057.) 

The  plates  are  each  surrounded  by  a  sheet  of  asbestos 
paper,  and  are  separated  from  each  other  by  a  thin  wooden 


BATTEHIES.  1777 

strip  so  thoroughly  perforated  with  large  holes  that  it 
really  fills  little  of  the  space  between  the  plates;  this  wooden 
strip  serves  as  a  distance-piece,  keeping  the  plates  a  certain 
fixed  distance  apart. 

2775.  The  E.  M.  F.  and  action  of  this  form  of  accu- 
mulator are  the  same  as  that  of  the  Faure  (pasted)  type  or 
the  Plante.  It  is  claimed  by  the  manufacturers  that,  from 
the  solidity  of  the  construction,  buckling  and  loosening  of 
the  active  material  are  practically  impossible,  so  that  the 
cells  may  be  discharged  to  a  low  E.  M.  F.  or  at  high  rates 
without  serious  injury.  Its  output  per  pound  of  element  is 
greater  than  that  usually  assigned  to  lead  accumulators,  be- 
ing about  5  ampere-hours  per  pound  of  plates  (both  positive 
and  negative)  at  normal  discharge  rates. 

2776.  Most  of  the  larger  installations  of  accumulators 
in  central  stations  in  this  country  have  been  of  this  type  of 
cell,  and  they  are  in  use  in  France  on  street-cars,  and  also 
in  England.  The  majority  of  German  installations  are  of 
the  pasted-plate  type. 

2777.  There  are,  as  in  primary  cells,  a  great  number 
of  forms  of  accumulators  in  use,  both  of  the  Plante  type  and 
the  Faure ;  they  differ  from  those  described  only  in  details 
of  construction,  such  as  the  arrangement  of  the  plates,  ver- 
tically or  horizontally,  the  form  of  the  grids,  etc.,  and  need 
not  be  described  here. 


BIMETALLIC    ACCUMULATORS. 

2778.  In  this  class  of  cells  the  elements  consist  of 
two  different  metals,  the  electrolyte  being  a  salt  of  one  of 
the  metals. 

There  have  been  several  combinations  of  materials  pro- 
posed for  cells  of  this  type,  but  the  only  cells  which  have 
actually  been  used  to  any  extent  are  the  zinc-lead,  copper- 
lead,  and  copper-zinc  cells. 

2779.  The  zinc-lead  cell  usually  consists  of  plates  of 
zinc  and  lead  in  a  solution  of  zinc  sulphate.     On  sending  a 


1778  BATTERIES, 

charging  current  through  this  cell  (the  zinc  being  the  nega- 
tive plate)  the  zinc  sulphate  is  decomposed,  depositing  zinc 
on  the  zinc  plate  and  forming  free  sulphuric  acid  with  the 
hydrogen  of  the  water,  which  is  also  decomposed,  its  oxygen 
uniting  with  the  lead  plate,  forming  peroxide  of  lead.  On 
open  circuit  and  while  charging,  the  free  sulphuric  acid  in 
the  solution  slowly  attacks  the  deposited  zinc,  reforming 
zinc  sulphate,  so  that  the  efficiency  of  this  form  of  cell  is 
low,  and  it  will  not  retain  a  charge  more  than  a  few  days. 
The  E.  M.  F.  is  high,  being  about  2.35  volts. 

2780.  The  more  modern  forms  of  this  cell  employ  a 
tinned-iron  plate,  amalgamated,  or  a  lead  plate,  in  place  of 
the  zinc  plate.  On  charging  the  cell  the  zinc  is  deposited  on 
the  surface  of  the  tinned-iron  or  lead  plate,  where  it  acts  as 
the  negative  plate  on  discharge.      (See  Art.  2726.) 

2T81.  By  substituting  copper  sulphate  for  zinc  sul- 
phate, and  copper  plates  for  the  zinc  or  other  negative 
plates  in  this  type  of  cell,  the  acid  formed  during  charge  can 
not  attack  the  copper,  so  that  this  loss  is  obviated;  the 
E.  M.  F.,  however,  is  but  1.25  volts  under  these  circum- 
stances, so  the  watt  output  is  materially  reduced. 

2782.  Owing  to  the  variations  in  the  composition  of 
the  electrolyte,  the  internal  resistance  of  cells  of  the  types 
before  described  is  variable,  being  lowest  when  charged 
and  increasing  during  discharge  as  the  sulphuric  acid  forms 
sulphate  of  copper  or  zinc. 

2783.  The  copper-zinc  accumulators  are  in  greater 
commercial  use  than  the  other  forms  of  bimetallic  cells,  the 
best  known  being  the  Phillips-Entz  accumulator,  which 
was  made  by  the  Waddell-Entz  Electric  Company.  This 
accumulator  employs  the  same  active  materials  as  the  La- 
lande-Chaperon  or  Edison-Lalande  primary  cell  (see  Arts. 
2683  and  2684),  modified  in  mechanical  construction  to 
adapt  them  for  accumulator  use. 

2784.  The  positive  plate  is  made  of  porous  copper  on 
a  solid  foundation,  prepared  in  the  following  manner,*     A 


BATTERIES.  1779 

copper  wire  is  surrounded  with  a  paste  made  of  finely  ground 
copper  oxide  and  sulphur;  around  this  is  woven  a  netting  of 
fine  copper  wire,  and  the  whole  is  then  heated  nearly  to  red 
heat,  which  causes  the  sulphur  to  unite  with  the  oxygen  of 
the  copper  oxide  and  pass  off  as  gas,  leaving  the  copper  on 
the  central  wire  in  a  very  porous  state.  This  cable  is 
covered  with  a  thin  layer  of  loosely  woven  cotton  thread, 
which  forms  a  porous  partition,  and  is  then  wound  or  braided 
into  a  mat  or  plate,  forming  the  positive  plate,  the  negative 
plate  being  a  thin  sheet  of  steel,  thoroughly  amalgamated; 
a  number  of  these  plates  are  mounted,  alternately  positive 
and  negative,  in  a  jar  made  of  sheet  steel,  and  surrounded 
by  the  electrolyte,  which  is  a  solution  oi  potassium  zincate 
2ind  potassium  hydrate.     (See  Arts.  2683  and  2689.) 

The  jar  is  covered  with  an  air-tight  steel  cover,  to  pre- 
vent the  carbon  dioxide  (carbonic  acid  gas)  in  the  air  from 
coming  in  contact  with  the  potassium  hydrate  solution; 
this  cover  is  provided  with  a  gas-valve  to  allow  the  gases 
formed  in  the  cell  to  pass  off. 

2785.  On  charging  the  cell  as  thus  constructed,  the 
chemical  reactions  are  complicated,  but  result  in  the 
deposition  of  the  zinc  from  the  potassium  zincate  on  the 
steel  plate  and  the  sides  of  the  jar,  and  the  oxidation  of  the 
porous  copper.  On  discharge  the  action  is  the  same  as  in 
the  Lalande-Chaperon  primary  cells;  that  is,  the  zinc  is  dis- 
solved, the  potassium  zincate  is  reformed,  and  the  copper 
oxide  reduced  to  metallic  (spongy)  copper. 

2786.  The  efficiency  of  this  type  of  accumulator  is 
about  the  same  as  that  of  the  lead  accumulators,  while  its 
output  is  very  much  greater,  weight  for  weight,  the  ampere^ 
hour  output  being  about  5  times  that  of  a  lead  cell,  or  about 
20  ampere-hours  per  pound  of  plates.  The  E.  M.  F.  of  this 
form  of  accumulator  being  much  lower  than  that  of  the  lead 
accumulator,  averaging  0.75  volt  during  discharge,  the 
comparison  on  a  basis  of  watt  output  is  not  so  favorable; 
still,  the  zinc-copper  accumulator  will  show  an  output  of 
about  15  watt-hours   per    pound   of  plates,   while  the  lead 


1780  .  BATTERIES. 

accumulators  seldom  exceed  an  output  of  from  7  to  10  watt- 
hours  per  pound  of  plates,  the  latter  figure  being  seldom 
reached  at  normal  rates  of  discharge. 

2787.  The  efficiency  and  internal  resistance  of  the. 
copper-zinc  accumulator  vary  quite  largely  with  the  tem- 
perature, on  account  of  the  considerable  variations  in  the 
density  of  the  electrolyte;  on  this  account  the  cells  are 
ordinarily  charged  and  discharged  at  a  temperature  of  about 
54°  C.  (130°  F.),  at  which  point  the  resistance  is  about  the 
same  as  in  a  similar  lead  accumulator. 

2788-.  These  cells  are  not  much  affected  by  the  rate  of 
discharge,  there  being  no  such  occurrence  as  sulphating  or 
buckling;  but  on  account  of  the  difficulty  of  depositing  the 
zinc  in  a  solid  form,  the  charging  must  be  done  at  a  slow 
rate,  and  the  action  of  the  cells  is  improved  by  intermittent 
charging.  The  E.  M.  F.  required  to  charge  one  of  these 
cells  varies  from  0.90  volt  at  the  start  to  1.05  volts  at  the 
finish. 

2789.  In  spite  of  the  porous  partition  (cotton  thread) 
which  surrounds  the  positive  plate,  local  action  is  liable  to 
occur,  on  open  circuit,  so  that  these  cells  will  not  retain 
their  charge  for  more  than  a  few  days,  while  a  lead  accu- 
mulator will  scarcely  lose  25^  of  its  charge  in  as  many  months. 

2790.  On  account  of  these  features  the  copper-zinc 
accumulator  can  be  successfully  used  only  in  installations 
where  it  is  charged  and  discharged  daily,  thus  preventing 
local  action,  and  when  it  can  have  the  necessary  appliances, 
care  and  attention  in  charging,  to  insure  proper  charging 
rate,  temperature,  etc. ;  so,  in  spite  of  its  large  output  per 
unit  of  weight,  it  can  hardly  come  into  general  use.  How- 
ever, for  traction  work,  that  is,  for  use  on  street-cars  and 
other  vehicles  in  constant  use,  where  the  accumulators  must 
be  able  to  stand  variable  and  very  frequently  heavy  dis- 
charge rates,  and  must  also  be  as  light  as  possible,  this  form 
of  accumulator  possesses  especial  advantages,  and  is,  con- 


BATTERIES.  1781 

sequently,  better  suited  to  the  work  than  the  lead  accumu- 
lator. 

2T91.  Other  forms  of  bimetallic  accumulators  have 
been  proposed,  and  in  some  cases  used,  among  which  may- 
be classed  several  forms  of  primary  cells,  such  as  the  Dan- 
iell,  Leclanche,  and  others,  which  may  be  "regenerated" 
by  passing  a  current  through  them;  these  have  never  been 
of  commercial  value,  and  do  not  require  further  attention. 


THE    USES    OF    ACCUMULATORS. 

2792.  In  central  stations  furnishing  electric  current 
for  lighting  and  other  purposes,  the  demand  for  current 
varies  very  largely  at  different  periods  in  the  day;  for 
example,  a  lighting  station  in  a  large  city  would  probably 
be  called  upon  to  furnish,  from  7  to  8  p.  m.,  10  times  the 
amount  of  current  that  was  required  from  7  to  8  a.  m.  ,  and 
in  smaller  stations  the  disproportion  is  even  greater.  As 
economy  of  operation  demands  that  the  engines  and  dyna- 
mos be  worked  at  or  near  their  full  capacity,  especially  if 
the  engines  be  compound  or  triple  expansion,  these  condi- 
tions can  both  be  met  only  by  dividing  the  machinery  into 
a  large  number  of  small  units,  or  by  having  some  system  of 
storage  of  the  electrical  energy.  In  the  first  case,  the  small 
units  require  more  attention,  and  are  much  less  efficient 
than  larger  ones,  and  most  modern  large  stations  have 
their  machinery  divided  into  a  few  large  units,  employing 
large  compound  or  triple-expansion  engines. 

2793.  In  these  stations  accumulators  are  being  intro- 
duced on  a  large  scale,  and  are  installed  according  to  one 
of  two  plans,  as  follows: 

1,  The  dynamos  and  engines  are  not  capable  of  carrying 
the  full  current  required  at  certain  parts  of  the  day,  for  ex- 
ample, in  the  evening,  but  are  of  a  size  sufficient  to  fur- 
nish the  current  for  the  average  rate  required  during  the 
24  hours.  In  this  case,  accumulators  are  installed  which 
have  a  capacity  sufficient  to  furnish  the  required  excess  of 


1782  BATTERIES. 

current  over  the  average.  At  times  when  the  output  of  the 
station  is  less  than  the  average  rate,  the  current  is  used  to 
charge  the  accumulators,  thus  keeping  the  output  of  the 
engines  and  dynamos  at  its  maximum,  which  is  the  condi- 
tion of  greatest  economy  in  operation.  On  account  of  the 
loss  in  charging  and  discharging  the  accumulators,  the 
machinery  must  really  have  a  capacity  slightly  greater  than 
the  average  output  of  the  station ;  but  in  any  case  the  total 
amount  of  machinery,  including  engines,  boilers,  and  dyna- 
mos, that  must  be  installed  is  far  less  than  if  accumulators 
were  not  used,  as  in  such  case  the  total  capacity  of  the 
machinery  must  evidently  equal  the  maximum  output  of 
the  station. 

2.  The  second  plan  is  to  install  accumulators  of  sufficient 
eapacity  to  furnish  all  the  current  of  the  station  for  a  part 
of  the  day  when  the  output  is  less  than  the  average;  in  this 
case,  the  engines  are  shut  down  for  a  considerable  part  of 
the  day,  the  accumulators  furnishing  the  entire  output  of 
the  station  during  this  time;  when  the  demand  for  current 
begins  to  increase,  the  machinery  is  started  up,  and  then 
furnishes  the  entire  output  of  the  station  for  the  balance  of 
the  day,  charging  the  accumulators  when  the  station  output 
is  less  than  the  capacity  of  the  machinery.  In  this  case  the 
capacity  of  the  accumulator  plant  is  relatively  less  than  in 
the  former,  and  as  the  cost  of  accumulators  is  high,  this 
may  cause  a  saving  over  the  first  plan,  although  the 
mechanical  efficiency  of  the  station  may  be  somewhat  lower 
than  in  the  first  case. 

2794.  The  result  of  applying  accumulators  to  a  large 
station  is  shown  in  Figs.  1065  and  1066.  In  both,  the  con- 
tinuous line  represents  the  actual  output  in  amperes  of  a 
certain  large  station  in  New  York,  for  a  certain  day. 

2795.  If  this  station  were  designed  to  use  accumula- 
tors according  to  the  first  plan,  the  result  would  be  about 
as  represented  in  Fig.  1065.  Here  the  dotted  line  repre- 
sents the  output  of  the  dynamos  (in  amperes) ;  the  differ- 
ence between  the  ampere  output  of  the  dynamos  and  that 


BATTERIES. 


1783 


of  the  station  is  either  absorbed  or  given  out  by  the 
accumulators,  as  the  station  output  is  less  or  greater  than 
the  dynamo  output.  From  the  curve  it  appears  that  the 
accumulators  are  absorbing  current  (that  is,  being  charged) 
from  about  11.45  p.  m.  to  about  4.30  p.  m.  (of  the  next  day), 
while  during  the  balance  of  the  24  hours  the  accumulators 
are  giving  out  current,  that  is,  discharging.  The  output  of 
the  dynamos  is  nearly  constant,  at  about  850  amperes,  the 


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output  for  the  24  hours  being  about  20,400  ampere-hours. 
The  output  of  the  station  is  20,000  ampere-hours,  the 
average  output  being  about  835  amperes.  This  shows  a  loss 
in  charging  of  400  ampere-hours,  which,  alloAving  for  slight 
overcharging,  etc.,  is  about  right,  as  the  capacity  of  the 
accumulator  plant  is  5,000  ampere-hours,  about.  This  station 
would  probably  have  installed  three  dynamos,  each  of  about 
450  amperes  output,   two  of  which  would  be  kept  running 


1784 


BATTERIES. 


all  the  time.  To  allow  of  cleaning,  inspection,  etc.,  one 
machine  would  be  replaced  from  time  to  time  by  the  machine 
which  had  been  previously  idle,  so  that  all  three  machines 
would  come  in  for  an  equal  amount  of  work.  In  case  of 
accident  to  one,  the  other  two  would  be  kept  running  until 
repairs  were  made;  the  accumulators  would  then  furnish  the 
current  for  such  brief  shut-downs  of  the  dynamos  as  would 
be  necessary  if  made  at  periods  of  light  load. 

2796.  If  the  accumulators  were  installed  according  to 
the  second  plan,  the  output  curve  would  be  represented  by 
Fig.  1066.     Here  all  the  dynamos  would  be  shut  down  from 


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2  until  8  A.  M.,  the  previously  charged  accumulators  furnish- 
ing the  output  of  the  station  during  that  time.  At  8  a.  m., 
in  this  case,  the  dynamos  would  be  started,  supplying  both 


BATTERIES.  1785 

the  output  of  the  station  and  sufficient  current  to  recharge 
the  accumulators.  AVhen  the  accumulators  are  fully 
charged,  they  are  disconnected  from  the  circuit  until  re- 
quired the  next  day.  In  this  case,  this  is  done  at  about 
4.40  p.m.,  the  output  of  the  station  from  this  time  being 
furnished  by  the  dynamos,  more  being  connected  in  circuit 
to  furnish  the  extra  output  during  the  evening.  In  this 
particular  case,  the  station  would  probably  have  installed 
five  dynamos,  each  of  a  capacity  of  about  500  amperes;  two 
of  these  would  be  of  sufficient  capacity  to  run  the  station 
from  8  A.M.  until  about  5  p.m.,  at  which  time  two  more 
would  be  switched  in;  the  first  two  would  then  be  shut  down 
when  the  output  was  reduced  sufficiently  to  permit ;  in  this 
case  one  would  be  shut  down  at  about  10  p.  m.  and  the 
other  at  about  11.30.  The  extra  dynamo  is  provided  to  use 
in  case  one  of  the  others  becomes  disabled.  The  station 
output  is,  as  before,  30,000  ampere-hours;  the  dynamo 
output  is  about  20,150  ampere-hours, the  loss  in  charging 
being  150  ampere-hours.  The  capacity  of  the  accumulator 
plant,  in  this  instance,  is  evidently  much  smaller  than  before, 
being  but  about  1,G00  ampere-hours;  the  dynamo  plant  is 
rather  more  than  proportionately  larger,  as  the  machines  do 
not  run  under  so  uniform  a  load  as  in  the  previous  case. 

In  this  arrangement  the  dynamos  do  not  operate  quite  so 
economically  as  in  the  first,  but  the  accumulators  operate 
more  economically,  being  charged  and  discharged  at  fairly 
uniform  rates,  while  in  the  previous  case  the  accumulators 
are  discharged  at  a  more  rapid  rate  than  they  are  charged, 
and  the  inaxinimn  discharge  rate  is  much  higher  than  the 
avei^age.  This  either  results  in  a  short  life  for  the  accumu- 
lators, consequently  a  high  allowance  for  depreciation,  or 
necessitates  a  larger  accumulator  plant  than  the  output  in 
ampere-hours  would  seem  to  require,  which  makes  the  first 
cost  high ;  again,  in  the  first  case,  the  firemen,  engineers, 
etc.,  would  be  required  to  be  in  attendance  during  the  whole 
of  the  24  hours,  which  would  probably  be  done  by  having 
three  "shifts,"  or  three  separate  gangs  of  men,  while  in  the 
seci)nd  case  no  firemen  or  engineers  are  required  during  the 


1786  BATTERIES. 

time  (from  2  until  8  a.  m.)  that  the  engines  and  dynamos 
are  shut  down,  so  two  "  shifts"  of  men  would  be  sufficient; 
hence,  it  would  appear  that  for  the  station  which  gave  this 
particular  output  curve  the  second  plan  of  installing  the  ac- 
cumulators would  be  preferable. 

2797.  Whether  or  not  it  would  pay  to  install  accumu- 
lators in  any  particular  station  depends  on  various  circum- 
stances, but  it  can  generally  be  determined  by  the  output 
curve,  actual  or  calculated,  from  which  may  also  be  deter- 
mined the  size  of  the  dynamos  and  accumulator  plants,  and 
the  proper  time  for  charging  and  discharging  the  battery, 
which  features  will  vary  largely  in  different  stations. 

2798.  In  railway  power  stations,  where  the  wide  varia- 
tions in  the  output  occur  from  second  to  second,  instead  of 
from  hour  to  hour,  as  in  lighting  stations,  accumulators 
would  serve  to  greatly  steady  the  load  on  the  generators, 
acting  on  somewhat  the  same  principle  as  does  a  heavy  fly- 
wheel on  an  engine;  the  accumulators  would  remain  at 
about  the  same  state  of  charge  continually,  if  properly  in- 
stalled, supplying  current  to  the  line  when  the  deniand  for 
current  is  heavy,  and  absorbing  energy  when  the  demand 
grows  light. 

2799.  Accumulators  would  be  especially  useful  if  the 
source  of  power  was  a  water-wheel,  since  they  would  make 
the  load  on  the  water-wheel  so  nearly  uniform  that  its 
regulation  would  be  good,  which  is  not  the  case  if  the  load 
is  irregular. 

2800.  Electrically  operated  street-cars,  in  which  the 
source  of  the  current  required  is  a  battery  of  accumulators, 
carried  upon  the  cars,  have  many  advantages  over  the  trolley 
system,  overhead  or  underground ;  the  disadvantages,  how- 
ever, are  so  serious  that  very  few  commercially  success- 
ful systems  of  this  kind  have  been  operated  in  this  country, 
although  several  lines  are  running  in  France  and  in  other 
parts  of  Europe. 


BATTERIES.  1787 

2801.  The  advantages  of  this  system  are  the  absence 
of  the  overhead  wires  or  underground  conduit  of  the  trolley 
roads,  the  complete  independence  of  each  car,  and  the  ability 
of  the  dynamos  which  charge  the  batteries  to  run  uniformly 
at  their  full  output. 

2802.  A  sufficient  number  of  accumulators  are  usually 
carried  on  one  car  to  run  it  about  30  miles,  or  for  about  six 
hours,  with  one  charging.  Such  a  battery  weighs  about 
4,000  to  4,500  lb.,  increasing  very  materially  the  weight  of 
the  car,  which  ordinarily  weighs,  with  passengers,  about 
10,000  lb.  The  power  required  to  propel  this  extra  weight 
must  be  provided,  and  the  wear  of  the  tracks  and  car-trucks 
is  increased. 

2803.  In  order  that  the  cars  shall  not  stand  idle  while 
its  battery  is  being  charged,  several  sets  (about  3  sets  to 
each  car)  are  provided,  which  makes  an  expensive  equip- 
ment, and  the  cost  of  handling  the  heavy  batteries,  when 
moving  them  into  and  out  of  the  cars,  is  considerable. 

2804.  The  chief  disadvantage,  however,  is  the  rapid 
deterioration  of  the  plates.  On  starting  the  car,  and  in  as- 
cending steep  grades  and  rounding  curves,  the  accumulators 
are  called  upon  to  furnish  currents  far  in  excess  of  their 
normal  discharge  rate,  which,  added  to  the  continual  jolting 
to  which  they  are  subject,  makes  the  disintegration  of  the 
positive  plates  very  rapid  indeed;  and  only  when  the  plants 
have  been  under  the  charge  of  skilled  experts  has  accumulator 
traction  been  at  all'  successful  in  this  country. 

2805.  The  Waddell-Entz  accumulator  would  seem  to  be 
especially  suited  to  traction  work,  on  account  of  its  light 
Aveight  and  capacity  for  high  rates  of  discharge;  but  to 
operate  efficiently,  this  accumulator  must  be  charged  and 
discharged  under  special  conditions  (see  Art  2790),  which 
makes  its  cost  of  operation  high. 

2806.  Accumulators  have  been  very  successfully  ap- 
plied to  launches  and  other  small  boats,  in  which  the  propeller 
is   driven  by  a  suitably  connected    motor;    the  battery  is 


1788  BATTERIES. 

located  under  the  seats  or  in  lockers,  and  is  usually  of  suf- 
ficient size  to  furnish  current  for  running  the  boat  at  a  speed  of 
seven  or  eight  miles  an  hour  for  about  40  miles;  higher  rates 
of  speed  can  be  obtained,  but  the  total  distance  covered  is 
then  lessened. 

2807.  In  general,  accumulators  have  been  more  or  less 
successfully  applied  (a)  where  it  is  desired  to  supply  a 
variable  demand  for  current  and  at  the  same  time  keep  the 
output  of  the  source  of  the  power  approximately  constant; 
{^)  where  it  is  desired  to  utilize  an  electric  current  at  a  point 
where  it  is  objectionable  or  impossible  to  obtain  the  current 
directly  from  dynamo  machines;  (r)  where  it  is  desired  to 
obtain  a  comparatively  small  but  continuous  current  from  a 
source  of  a  considerable  current,  which  can  be  utilized  only 
a  short  time  and  at  infrequent  intervals,  and  {d)  where  a 
perfectly  steady  current  is  required  for  certain  applications, 
where  the  current  from  dynamo  machines,  which  is  always 
slightly  irregular,  would  be  unsuitable. 

2808.  Under  (a)  would  be  classed  the  various  lighting 
and  power  station  installations,  the  principles  of  which  have 
been  described  (Art.  37'92).  An  extension  of  the  plan  of 
such  stations  has  been  adopted  abroad,  in  cases  where  a  con- 
siderable demand  for  current  from  a  (direct  current)  central 
station  occurs  in  some  particular  district,  at  a  distance  from 
the  station.  It  is  evident  that  if  this  demand  is  met  by 
sending  the  current  directly  from  the  station,  the  wires  for 
carrying  the  current  must  be  large  enough  to  carry  the 
maxiiHiini  current  required,  although  this  maximum  only 
continues  for  a  few  hours  in  each  day.  If  an  accumulator 
plant  be  installed  in  this  district,  the  wires  from  the  station 
need  only  be  large  enough  to  carry  the  average  current  re- 
quired for  that  district,  the  battery  furnishing  the  additional 
current  during  the  period  of  heavy  load  and  charging  when 
the  load  is  less  than  the  average,  just  as  in  the  first  plan  for 
installing  accumulators  in  central  stations.  (See  Arts. 
2792  and  2793.)     Aside  from  the  saving  in  the  wire, 


BATTERIES.  1789 

there  are  other  advantages  of  this  method  of  current  distri- 
bution, which  will  be  treated  of  in  another  section. 

2809.  Another  application  which  comes  under  this  same 
head,  although  carried  out  on  a  much  smaller  scale  than  the 
examples  given,  is  made  in  places  where  a  current  of  con- 
siderable strength  is  required  only  occasionally,  with  con- 
siderable intervals  between;  primary  cells  might  be  directly 
applied  in  such  cases,  but  on  account  of  their  high  in- 
ternal resistance  a  considerable  number  of  cells  or  a  few  very 
large  cells  would  be  required  to  furnish  the  necessary  cur- 
rent, or  else  local  action  would  soon  render  them  useless; 
if,  however,  primary  cells,  say  of  the  "gravity  "or  other 
type  giving  a  constant  E.  M.  F.,  be  used  to  charge  secondary 
cells,  the  charging  can  go  on  continuously  day  and  night  at 
a  slow  rate,  and  at  any  time  the  secondary  cells  may  be  drawn 
upon  for  a  considerable  current  far  beyond  the  capacity  of 
the  primary  cells  themselves.  This  method  is  often  adopted 
in  surgeons'  offices,  where  a  considerable  current  is  occa- 
sionally required  for  heating  cauteries  and  for  similar  work. 
(See  Arts.  2712  and  2714.) 

281 0.  Under  class  {b)  would  be  included  such  applica- 
tions of  accumulators  as  in  propelling  street-cars  and  small 
boats,  the  main  features  of  which  have  been  given.  (See 
Arts.  2800  and  2806.) 

281 1.  Under  this  same  head  would  also  be  classed  the 
transporting  of  electrical  energy  by  means  of  charged  ac- 
cumulators; these  are  usually  charged  at  some  central  sta- 
tion, and  are  then  carried  to  the  point  where  it  is  desired  to 
use  the  current.  Thus  far  this  has  been  done  only  on  a 
comparatively  small  scale,  principally  for  furnishing  current 
to  the  motors  which  drive  the  phonographs  and  kinetoscopes 
and  similar  machines,  which  are  so  generally  on  exhibition, 
often  in  localities  where  electric-light  circuits  are  not  avail- 
able, or  are  not  of  the  right  character, 

2812.  Under  class  {c)  may  be  included  several  of  the 
more  important  of  the  minor  applications  of  accumulators, 


1700  BATTERIES. 

as  follows:  The  electric  lighting  of  railroad-cars,  the 
charging  current  for  the  accumulators  being  obtained  from 
dynamo  machines  driven  from  one  of  the  axles  of  the  car, 
which  source  of  power  is  obviously  intermittent  and  irreg- 
ular; the  lighting  of  houses,  at  a  distance  from  electric- 
light  stations,  such  as  country  residences,  where  the  power 
for  driving  the  charging  dynamos  is  obtained  from  wind- 
mills or  the  action  of  the  waves  or  tides,  which  sources  of 
power  are  very  variable.  Special  devices  are  usually  used 
in  such  plants  which  automatically  disconnect  the  dynamo 
from  the  accumulators  when  the  source  of  power  has 
stopped,  or  is  insufificient  to  furnish  the  requisite  current  for 
charging.  The  lighting  and  furnishing  of  small  amounts  of 
power  to  the  offices  or  such  other  departments  of  mills  or 
factories  as  are  obliged  to  be  in  operation  when  the  main 
engine  or  other  source  of  power  is  shut  down,  the  accumu- 
lators being  charged  during  the  day,  when  the  main  engine 
is  running,  also  comes  under  this  head. 

2813.  The  amount  of  current  required  for  lighting  an 
ordinary  house  is  comparatively  little,  and  a  very  small 
engine  and  dynamo  would  readily  furnish  it;  but  the  noise 
and  trouble  of  operating  such  a  small  plant  at  the  time  when 
the  current  was  required  would  make  it  objectionable.  In 
such  a  case  an  accumulator  plant  may  be  installed,  of  sufH- 
cient  capacity  when  charged  to  furnish  the  current  for  light- 
ing for  several  days  or  even  weeks;  then,  by  installing  an 
engine  and  dynamo  of  proper  size,  the  battery  may  be 
charged  once  a  week  or  month,  as  the  case  may  be,  with 
comparatively  little  trouble  and  expense,  and  the  time  for 
charging  may  be  chosen  so  that  the  noise  or  other  features 
would  not  be  objectionable.  Such  a  plant  would  be  classed 
under  this  same  head,  (c). 

2814.  Under  (d)  would  be  classed  the  special  applica- 
tion of  accumulators  in  testing  and  in  telephone  work.  Their 
action,  as  regards  the  steadiness  of  the  current,  is  no  more 
favorable  than  that  of  a  good  primary  cell;  but  for  a  given 
output  the  accumulator  is  more  compact,  requires  less  at- 


BATTERIES.  1791 

tention,  and  its  elements  do  not  need  to  be  replaced  when 
exhausted,  but  renewed  by  a  charging  current.  Conse- 
quently, accumulators  are  coming  into  use  for  telephone 
central  stations,  where  three  or  four  good-sized  cells  may 
replace  several  hundred  primary  cells;  they  are  usually  in- 
stalled in  conjunction  with  suitable  charging  apparatus, 
usually  small  dynamos,  the  operation  of  charging  being 
gone  through  with  whenever  necessary. 

2815.  The  specific  applications  of  accumulators  cover 
many  more  cases  than  have  been  given;  but  they  may  be 
all  classed  under  these  several  heads. 


THE  INSTALLATION  OF  ACCUMULATORS. 

2816.  As  stated  in  Art.  2757,  accumulators  are  usu- 
ally of  approximately  cubical  form,  and  the  jars  are  usually 
of  glass  or  hard  rubber,  in  ordinary  sizes;  for  special  appli- 
cations, such  as  portable  cells  and  batteries  for  street-car 
and  launch  use,  special  jars  are  provided  to  suit  the  condi- 
tions. For  ordinary  installations  for  lighting  purposes,  the 
glass  jar  is  best  suited,  as  it  permits  the  examination  of  the 
interior  of  each  cell  at  any  time,  and  any  cells  in  which 
the  active  material  shows  signs  of  buckling  or  disintegra- 
ting may  be  attended  to  before  the  fault  becomes  serious, 

2817.  Accumulators  should  be  placed  on  racks  or 
shelves,  and  if  the  number  of  cells  be  large,  it  is  usually 
advantageous  to  place  them  in  several  tiers.  Plenty  of 
room  should  be  allowed  between  the  tiers,  to  allow  of 
making  connections,  taking  out  or  replacing  plates  or  the 
electrolyte,  etc. 

2818.  If  the  cells  are  located  in  a  room  where  the  air 
is  warm  and  moist,  water  will  collect  on  the  surface  of  the 
jars  and  shelves,  and  will  cause  an  appreciable  leakage  of 
the  current;  to  obviate  this,  each  cell  should  be  supported 
on  a  small  shelf,  which  should  rest  on  porcelain  or  glass 
insulators,  and  the  jars  of  adjacent  cells  should  not  be 
allowed  to  touch. 


1792  BATTERIES. 

2819.  If  exhaust  steam  is  to  be  had  for  heating  pur- 
poses,  a  double  line  of  pipes,  running  under  the  shelves  on 
which  the  cells  rest,  will  be  beneficial,  as  the  heat  will  cause 
a  circulation  of  the  electrolyte,  and  will  decrease  its  resist- 
ance. Such  an  arrangement  is  very  necessary  for  cells  of 
the  Waddell-Entz  type  (see  Art.  2783),  but  for  ordinary 
lead  accumulators  the  advantage  is  not  sufficient  to  warrant 
any  great  outlay  for  such  heating. 

2820.  The  space  to  be  allowed  for  a  battery  depends 
on  the  make  and  type,  and  may  usually  be  found  in  the 
catalogues  of  the  manufacturers.  Lead  accumulators  of 
ordinary  size  will  usually  have  a  capacity  of  2.5  to  4  ampere- 
hours  per  square  inch  of  floor  space  that  they  occupy;  for 
large  accumulators  in  lead-lined  boxes,  such  as  are  installed 
in  central  stations,  this  value  may  be  increased  to  5.  A  good 
average  figure  for  cells  of  200  to  500  ampere-hours  capacity 
is  3  ampere-hours  per  square  inch  of  fioor  space  occupied. 

The  output  per  cubic  inch  of  volume  is  rather  more  con- 
stant, being  about  .25  to  .3  ampere-hour.  The  weight  of  a 
battery  of  accumulators  is  considerable,  and*  the  shelves  or 
other  supports  intended  to  hold  them  should  be  made 
amply  strong,  for  if  they  sag  or  bend,  the  glass  jars  are 
liable  to  be  broken. 

2821.  The  electrolyte  of  an  accumulator  will  not  freeze 
until  exposed  to  a  temperature  of  about  —  11°  C.  (about  13° 
F.);  freezing  should  be  avoided,  as  it  is  very  liable  to  break 
the  jars. 

2822.  The  number  of  cells  required  for  any  given  in- 
stallation depends  upon  the  E.  M.  F.  desired ;  ordinary  light- 
ing plants  are  usually  designed  for  an  E.  M.  F.  of  50  to  55 
or  100  to  120  volts.  The  number  of  accumulators  required 
may  be  found  by  dividing  the  E.  M.  F.  required  by  the 
average  E.  M.  F.  of  the  cell  during  discharge,  which  is 
usually  taken  (for  lead  accumulators)  as  1.9  volts;  a  55-volt 

55 
installation    would  then  require  — —  =  29    cells    (obviously, 

fractional  cells  are  an  impossibility). 


BATTERIES.  1793 

2823.  When  only  partially  discharged,  the  E.  M.  F.  of 

such  a  battery  would  be  higher  than  that  required;  this  may 
be  reduced  by  placing  a  suitable  resistance  in  series  with 
the  battery,  and  adjusting  this  as  the  E.  M.  F.  diminishes,  to 
keep  a  constant  E.  M.  F,  at  the  lamps,  or  arranging  the 
connections  so  that  one  or  more  cells  may  be  cut  into  circuit 
from  time  to  time,  to  effect  the  same  result. 

Manufacturers  of  electrical  apparatus  furnish  devices 
which  will  automatically  perform  the  above  operations  as 
the  E.  M.  F.  of  the  battery  changes. 

2824.  To  allow  for  possible  accidents  to  one  or  more 
cells,  and  for  the  drop  in  the  wiring  and  connections,  one  or 
two  extra  cells  may  be  provided,  and  so  arranged  that  they 
may  be  cut  into  the  circuit  at  any  time. 

2825.  The  size  of  each  cell  in  such  an  installation  de- 
pends upon  the  strength  of  the  current  which  it  is  desired 
to  use,  and  the  length  of  time  (number  of  hours)  the  cur- 
rent is  required;  thus,  to  furnish  a  current  of  10  amperes 
for  10  hours  with  one  charging  would  require  cells  of  a 
capacity  of  10  X  10  =  100  ampere-hours  each. 

2826.  The  current  required  for  operating  incandescent 
lamps,  the  average  number  of  hours  per  day  that  they  are 
lighted,  etc.,  will  be  treated  of  later,  and  from  the  values 
given,  the  size  and  number  of  accumulators  which  should  be 
installed  to  furnish  the  current  for  lighting  a  building  may 
be  determined. 

2827.  The  method  of  procedure  in  setting  up  the 
ordinary  forms  of  cells  is  about  as  follows: 

Having  prepared  the  shelves  or  supports  for  the  cells, 
unpack  and  thoroughly  clean  the  jars,  and  place  them  in 
position  on  the  shelves,  with  the  support  for  the  plates 
(5,  5,  Fig.  1057)  in  place.  The  plates  should  then  be  thor- 
oughly cleaned  of  the  sawdust  in  which  they  were  packed, 
and  placed  in  position  in  the  jars.  They  should  rest  evenly 
on  the  supports  which  raise  them  from  the  bottom  of  the 
jar,  and  the  blocks  or  strips  of  insulating  material  which 


1794  BATTERIES. 

separate  the  plates  should  be  properly  placed  in  position 
between  them.  In  some  makes  of  cells  pieces  of  rubber  or 
glass  tubing  are  used  for  this  purpose. 

2S28.  The  plates  should  be  so  placed  in  the  jars  that 
the  connecting  strips  will  come  into  the  proper  position  for 
connecting  the  positive  plates  of  one  cell  to  the  negative  of 
the  next,  and  so  on. 

The  joints  between  the  connecting  strips  should  then  be 
made  bright  and  smooth,  for  which  purpose  a  fine  file  or 
sandpaper  is  best;  the  connecting  bolts  should  be  set  up 
with  a  good  pressure,  so  that  these  bright  surfaces  will  be 
squeezed  together  firmly,  insuring  good  contact. 

2829.  The  electrolyte  should  be  prepared  in  a  lead- 
lined  or  stoneware  tank,  and  the  sulphuric  acid  should  be 
slowly  poured  into  the  water  and  thoroughly  stirred  until 
the  solution  is  of  the  proper  density  (1.17  sp.  gr. ).  It  is 
well  to  note  that  water  should  never  be  poured  into  sul- 
phuric acid;  as  the  two  liquids  combine  with  considerable 
heat,  the  small  quantity  of  water  which  first  reaches  the 
acid  is  instantly  converted  into  steam,  resulting  in  an 
explosion,  which,  by  scattering  the  acid  about,  is  liable  to 
cause  serious  injury.  Therefore,  in  preparing  the  electro- 
lyte,  always  pour  the  acid  into  the  water. 

In  case  a  considerable  quantity  of  solution  is  to  be  pre- 
pared, blocks  of  piire  ice  (manufactured  ice  is  best)  may  be 
used  in  place  of  water.  The  heat  generated  by  the  dilution 
of  the  acid  is  then  absorbed  in  melting  the  ice. 

2830.  When  all  connections  are  made  and  preparation 
for  charging  completed,  the  electrolyte  should  be  poured 
into  the  cells  until  the  plates  are  covered  to  a  depth  of  half 
an  inch  or  so,  and  as  soon  as  possible  thereafter  the  cells 
should  be  charged.  If  allowed  to  stand  uncharged  in  the 
acid,  the  plates  are  liable  to  become  sulphated  (see  Art. 
2736).  Care  should  be  taken  that  the  charging  current 
is  of  the  right  polarity;  that  is,  that  the  current  ^o\Js  from 
the  positive  to  the  negative  plates  through  the  cell;  if  this 
is  reversed,  the  cells  will  be  reversed,  and  a  great  deal  of 


BATTERIES.  1795 

trouble  -will  be  experienced  in  getting  them  back  to  thfe 
proper  condition. 

The  first  charging  should  be  long  continued  and  at  a  low 
rate,  to  remove  any  sulphate  that  may  exist. 

2831.  In  charging  an  accumulator,  as  has  been  shown, 
only  a  small  part  (about  Sfo)  of  the  E.  M.  F.  required  to 
force  the  current  through  the  cell  is  expended  in  overcom- 
ing the  resistance  of  the  plates  and  electrolyte  ;  the 
remainder  is  expended  in  overcoming  the  E.  M.  F.  of  the 
chemical  action  of  the  cell.  It  follows,  then,  that  if  the 
applied  E.  M.  F.  be  just  equal  to  the  E.  M.  F.  of  the  cell 
no  current  will  flow  (see  Art.  2504),  so  that  the  E.  M.  F. 
of  the  cell  itself  may  be  considered  as  a  counter  E.  M.  F., 
opposing  that  of  the  charging  current.     To  apply  Ohm's 

law  (  ^  =  "d  )  to  this  case,  the  E  must  be  considered  as  repre- 
senting the  algebraic  sum  of  the  applied  and  the  counter 
E.  M.  F. ,  or  ^  =  applied  E.  M.  F.  —  counter  E.  M.  F.  This 
is  merely  another  way  of  stating  that  the  E.  M.  F.  required 
tb  drive  the  charging  current  through  the  cell  is  only  that 
required  to  overcome  its  ohmic  resistance;  but  to  this  must 
be  added  an  E.  M.  F.  equal  and  opposite  to  the  E.  M.  F.  of 
the  cell  itself,  due  to  the  chemical  affinity  of  the  substances 
of  which  it  is  composed. 

In  charging,  then,  if  from  any  cause  the  E.  M.  F.  of  the 
charging  current  be  changed  by  a  small  amount,  the  char- 
ging current  will  be  altered  in  a  much  greater  degree, 
depending  on  the  ratio  between  the  applied  E.  M.  F.  and 
the  difference  between  the  applied  and  counter  E.  M.  F. 
For  example,  consider  a  cell  which  has  been  discharged 
until  its  E.  M.  F.  is  1.925  volts  (on  open  circuit).  The 
resistance  of  the  cell  is  .005  ohm  and  its  normal  charging 
current  is  35  amperes.  The  drop  due  to  this  current  is 
35  X  .005  =  .175  volt;  the  applied  E.  M.  F.  must  then  be 
1.925  + -175  =  2.10  volts,  to  cause  35  amperes  to  flow. 
Now,  if  the  applied  E.  M.  F.  drops  to  2.0  volts,  it  is  evident 
that,  the  counter  E.  M.  F.  being  the  same,  the  drop  is  equal 


1796  BATTERIES. 

to  2.0  —  1.925  =  .075  volt,   and  the    current    which    would 

cause  this  drop  when  flowing  against  .005  ohm  resistance  is 

E        075 
C  =^-^  ^'—-—  —  1^  amperes.      Thus,  a  drop  in  the  applied 

E.  M.  F.  of  -^,  or  about  5fo,  causes  the  current  to  fall  off 
2. 1 

more  than  50^. 

This  shows  the  necessity  for  having  the  source  of  the 
charging  current  so  arranged  that  the  E.  M.  F.  may  be 
closely* adjusted  in  order  that  the  charging  current  may  be 
maintained  at  its  proper  value. 

In  all  accumulator  plants  of  any  considerable  capacity 
the  source  of  the  charging  current  is  a  dynamo,  and  the 
methods  of  attaining  this  adjustment  therewith  will  be 
given  later.  In  any  case,  the  maximum  E.  M.  F.  of  the 
source  of  the  charging  current  must  be  higher  than  the 
highest  counter  E.  M.  F.  that  the  tattery  can  give. 

2832.  With  every  accumulator  plant  2^  hydrometer  (see 
Art.  995)  should  be  included,  as  the  electrolyte  should  be 
kept  at  the  proper  density.  The  state  of  charge  of  the  cell 
can  be  approximately  determined  by  the  density  of  the 
electrolyte  (see  Art.  2737). 

2833.  The  volume  of  the  electrolyte  will  gradually 
diminish  during  the  operation  of  the  cell,  due  to  evapora- 
tion and  to  the  evolution  of  gas  when  the  cell  is  charged; 
this  loss  should  be  made  up  by  occasionally  adding  pure 
water,  or  acid,  if  the  density  as  indicated  by  the  hydrometer 
is  too  low. 

2834.  A  portable  voltmeter  should  also  be  provided, 
which  shall  have  a  capacity  such  that  the  E.  M.  F.  of  a 
single  cell  may  be  accurately  measured,  so  that  if  the  action 
of  any  cell  seems  to  be  irregular,  its  condition  may  be  de- 
termined by  measuring  its  E.  M.  F.  and  comparing  it  with 
that  of  the  other  cells.  Some  instrument  makers  furnish 
portable  voltmeters  with  two  scales,  one  a  tenth  or  a  twen- 
tieth the  value  of  the  other;  these  are  very  convenient  for 
accumulator   work,   as  by  selecting   the   proper   scale   the 


BATTERIES,  1797 

E.  M.  F.  of   the  entire  battery  or  of   single  cells  may  be 
accurately  determined. 

2835.  Accumulators  should  not  be  installed  near  any 
apparatus  which  has  bright  metal  surfaces,  such  as  an 
engine,  as  the  fumes  from  the  acid  will  corrode  such  sur- 
faces unless  they  are  protected  by  a  coating  of  grease  or 
varnish ;  all  connectors  and  other  brass  pieces  used  around 
the  cell  should  be  coated  with  varnish  or  grease  for  the 
same  reason.  Vaseline  is  especially  applicable  for  this 
purpose. 

This  effect  may  be  largely  prevented  by  providing  the 
cells  with  covers,  which  also  prevents  evaporation  to  a  large 
extent.  Covering  the  liquid  with  a  layer  of  heavy  oil  has 
also  been  proposed,  but  this  plan  involves  a  great  deal  of 
troublesome  dirtiness,  as  the  bubbling  of  the  escaping  gas 
causes  the  oil  to  spatter. 


APPLIED    ELECTRICITY. 

(CONTINUED.) 


THEORY  OF   THE  DYNAMO. 

3015.  In  order  that  a  current  may  flow  through  a 
circuit,  and  thereby  be  available  for  doing  work,  it  is  nec- 
essary that  a  difference  of  potential  be  established  between 
two  points  in  that  circuit,  and  in  order  that  the  resulting 
current  may  be  maintained,  it  is  necessary  to  maintain  the 
difference  of  potential  between  these  points,  (See  Art. 
2237.) 

This  difference  of  potential  may  be  established  and  main- 
tained in  a  variety  of  ways,  some  of  which — the  chemical 
action  of  certain  liquids  on  certain  other  substances,  for 
example — have  already  been  explained. 

Generating  an  E.  M.  F.  in  a  conductor  by  moving  the 
conductor  in  a  magnetic  field  in  such  a  direction  that  it  cuts 
the  lines  of  force  of  the  field,  is  by  far  the  most  extensively 
used  method  of  establishing  the  required  difference  of  poten- 
tial, and  a  machine  for  generating  and  maintaining  an 
E.  M.  F.  by  the  movement  of  one  or  more  conductors  across 
the  lines  of  force  of  a  magnetic  field   is  called  a  dynamo. 

3016.  The  amount  of  the  E.  M.  F.  generated  in  a  mov- 
ing conductor  depends  upon  the  rate  at  which  the  conductor 
cuts  the  lines  of  force.  (Art."  2449.)  With  practicable 
values  for  the  length  of  the  conductor,  for  its  velocity,  and 
for  the  extent  and  density  of  the  magnetic  field,  the  E.  M.  F. 
which  can  be  generated  in  a  single  conductor  is  not  sufficient 
for  most  of  the  applications  of  the  electric  current.  How- 
ever, by  joining  a  number  .of  conductors  in  series,  in  such  a 

For  notice  of  copyright,  see  page  immediately  following  the  title  page. 


1898  APPLIED   ELECTRICITY. 

manner  that  the  E.  M.  F.'s  generated  in  them  are  added 
together,  any  desired  E.  M.  F.  may  be  obtained. 

The  character  of  the  E.  M.  F.  of  a  dynamo  depends  upon 
the  grouping  of  the  various  conductors  with  respect  to  the 
magnetic  field,  and  to  the  method  of  connecting  these  con- 
ductors with  the  external  circuit. 

The  part  of  the  dynamo  in  which  the  E.  M.  F.  is  gener= 
ated,  consisting  of  the  conductors,  the  means  of  supporting 
and  moving  them,  and  the  device  for  connecting  them  with 
the  external  circuit,  is  called  the  armature,  and  the  con- 
ductors, in  their  various  arrangements  and  connections,  con- 
stitute the  armature   winding. 

The  effect  of  the  various  methods  of  arranging  and  con- 
necting armature  windings  upon  the  character  of  the  E.  M.  F. 
produced  may  best  be  studied  by  developing  them  from  the 
simplest  form,  a  straight  conductor  moving  in  a  straight 
line  through  a  uniform  magnetic  field,  as  will  be  explained 
later. ' 

3017.  The  principal  sources  of  magnetic  fields  are  per- 
manent magnets,  such  as  the  earth,  masses  of  lodestone,  or 
hard-steel  magnets,  and  electromagnets. 

As  the  E.  M.  F.  generated  in  a  moving  conductor  is  pro- 
portional to  the  density  of  the  field  in  which  it  moves,  other 
conditions  remaining  the  same,  it  is  obvious  that  a  field  of 
considerable  density  is  desirable.  For  this  reason  the  earth's 
field  or  that  of  permanent  magnets,  either  natural  or  artifi- 
cial, is  seldom  used  in  dynamo-electric  machinery,  since  the 
density  of  such  a  field  is  low  compared  with  that  possible  to 
obtain  with  suitably  designed  electromagnets,  so  that,  in 
spite  of  the  fact  that  electrical  energy  must  be  continually 
expended  in  order  to  keep  up  the  magnetizing  force  of  the 
electromagnet,  this  last  form  is  almost  universally  used. 

The  design  of  electromagnets  for  dynamo-electric  ma- 
chinery will  be  discussed  later;  for  the  present  it  is  sufficient 
to  consider  that  the  magnetic  field  exists  in  the  space  be- 
tween one  or  more  pairs  of  poles,  the  balance  of  the  mag- 
netic circuit  not  being  considered. 


APPLIED   ELECTRICITY.  1899 

GENERATION    OF    E.    M.    F. 

3018.  If  any  straight  conductor  a  b,  the  direction  of 
whose  length  is  at  right  angles  to  the  lines  of  force,  is  moved 
in  a  uniform  magnetic  field  in  a  direction  at  right  angles  to 
the  lines  of  force  of  the  field  and  to  its  own  length,  and  at 
such  a  uniform  velocity  that  at  the  end  of  unit  time  (1  sec- 
ond) it  reaches  the  position  a'  b' ,  as  represented  in  Fig.  1123, 
the  following  conclusions  result  : 

The  velocity  of  the  conductor  may  be  represented  by  the 
length  of  the  line  a  a'  (or  b  b'),  as  the  conductor  moves  over 
this    distance    in    unit    time.      The    total 
number  of  lines  cut  by  the  conductor  is   :■; 
evidently  that    number    enclosed    in    the   •: 
area  a  a'  b'  b ;  the  lines  a  a'  and  a  b  (or  b  b'   .': 
and  a'  b')   being  at  right   angles  to  each   ;'; 
other,  the  area  enclosed  by  aa'  b'  b  is  the   ■• 
product  of  the  length  of  the  conductor  a  b,    ■■' 
and   the   length  of  its  path  a  a'  (or  bb').    v. 
Formula    447,    given    in    Art.    2449,   '<'y, 


^IBH 


W 


E  =  — ^,  may  be  modified  to  fit  this  case,    ••••■•-•'•-••■= — 1>-- 

10   t  Fig.  1123. 

as  follows:  Let  B  =  the  density  of  the  magnetic  field,  L  = 
the  length  of  the  conductor,  and  iJ/=  the  length  of  its  path, 
or  its  velocity.  Then,  the  area  moved  over  by  the  con- 
ductor (in  unit  time)  is  L  M,  and  the  total  number  of  lines 
cut  by  the  conductor  is  B  -^  M-     Then,  substituting  this  value 

for  N  in  the  above  formula,  E  =  — -— ^ — .     As  in  this  case 

10' ^^ 

/  =  1,  unit  time  being  assumed,  this  may  be  written 

E^^f,  (473.) 

which  gives  an  expression  whereby  the  E.  M.  F.  generated 
in  a  conductor  moving  in  a  magnetic  field  under  the  con- 
ditions given  above  may  be  found. 

The  density  B,  being  the  number  of  lines  of  force  per  unit 
of  area,  i.  e.,  per  square  inch,  or  per  square  centimeter,  it  is 


1900 


APPLIED   ELECTRICITY. 


evident  that  the  product  L  M  must  be  expressed  in  the  same 
units  in  order  that  the  equation  N  =^  L  i^  should  hold  true. 

Example. — Suppose  the  conductor  a  b  \n.  Fig.  1123  to  be  1  foot  8 
inches  long,  and  that  it  is  moved  in  a  magnetic  field  whose  density  is 
50,000  lines  of  force  per  square  inch  at  such  a  (uniform)  velocity  that 
at  the  end  of  1  minute  it  would  have  moved  2,250  feet.  What  is  the 
E.  M.  F.  generated  in  the  conductor  ? 

Solution. — As  the  density  is  expressed  in  lines  of  force  per  square 
inch,  the  other  dimensions  must  be  reduced  to  the  same  unit,  i.  e., 
inches. 

The  length  of  the  conductor  L  is  then  20  inches,  and  the  velocity, 

2,250 


or  distance  through  which  it  would  move  in  1  second,  =  M  — 
37.5  ft.,  or  37.5  X  12  =  450.0  in. 


60 


Hence,  from   formula   473,  E ^^ ^J^,  where  B  =  50,000,  L  =  20, 


and  M  =  450,  E 


10« 
50,000  X  20  X  450      450,000,000 


10* 


10^ 


=  4.5  volts.     Ans. 


3019.  The  formula  given  in  Art.  3018  does  not  hold 
good  as  it  stands  if  the  conditions  governing  the  direction 
of  the  motion  of  the  conductor  are  not  as  before  stated, 
which  are,  that  the  conductor  must  lie  in  a  plane  at  right 
angles  to  the  lines  of  force  and  move  in  a  direction  at  right 
angles  to  its  own  length  and  to  the  direction  of  the  lines  of 
force.  It  is  evident  that  a  conductor  might  readily  be 
moved  in  a  direction  which  would  not  conform  to  all  or  any 
of  the  above  conditions;  the  formula,  to  be  generally  ap- 
plicable^ must  then  be  modified  to  suit  such 
cases. 


Tkkki'kkii 


/ 


K 


3020.  Fig.  1124  represents  a  case  where 
a  conductor  a  lies  in  a  plane  at  right  angles  to 
the  lines  of  force  (so  that  we  are  looking 
along  its  length,  and  consequently  see  only 
the  round  section,  as  shown),  and  is  moved 

^^  in  a  direction  at  right  angles  to  its  own 
length,  but  at  the  angle  /,  which  is  not  a 
right  angle,  to  the  direction  of  the  lines  of 

^  force  flowing  between  the  poles  A^  and  5  of 
Fig.  1124.         a  magnet.      If  the  conductor  move  from  a 


APPLIED   ELECTRICITY.  1901 

to  a  in  unit  time  (say  one  second),  the  area  swept  over  by 
the  conductor  in  unit  time  is  a  rectangle,  and  the  area  is 
measured  by  the  product  L  M  of  the  length  of  the  conductor 
L  and  the  length  of  its  path  in  unit  time,  or  its  velocity,  M\ 
but  the  total  number  of  lines  cut  by  the  conductor  is  not 
the  product  of  the  density  B  and  the  area  L  M,  since  the 
density  is  measured  on  a  plane  at  right  angles  to  the  lines 
of  force,  and  the  area  L  Mis  at  an  angle  to  this  plane. 

From  an  inspection  of  Fig.  1124,  it  will  be  seen  that  the 
conductor  will  cut  exactly  the  same  number  of  lines  of  force 
if  moved  from  any  point  on  the  line  a  n  (whicli  is  parallel  to 
the  lines  of  force)  to  the  point  a' ;  in  other  words,  whatever 
the  value  of  the  angle  /,  the  number  of  lines  of  force  cut 
by  the  conductor  in  moving  from  a  to  a'  will  be  the  same. 

By  making  this  angle  a  right  angle,  as  at  n,  the  path  of 
the  conductor  along  the  line  7t  a'  will  be  at  right  angles  to 
the  lines  of  force,  and  all  the  conditions  prescribed  in 
Art.  3018  will  be  fulfilled. 

The  length  of  the  line  n  a'  is,  however,  not  equal  to  the 
length  of  the  line  a  a';  but  as  the  former  length  must  be 
used  in  calculating  the  total  number  of  lines  cut,  and  the 
latter  is  the  length  which  is  known,  an  expression  for  the 
length  71  a'  in  terms  of  the  length  a  a'  must  be  found.  From 
the  construction  of  the  figure,  the  triangle  a  n  a'  is  a  right- 
angled  triangle,  with  the  length  of  the  hypotenuse  a  a' 
and  the  adjacent  angle/  given;  the  length  of  the  side  7t  a' 
opposite  the  angle  /  is  found  by  trigonometry  to  be  a  a'  sin 
p°,  which  is  the  desired  value.  ' 

3021.  Calling  the  length  of  the  conductor  L  and  the 
length  of  its  path  M,  as  before,  it  follows  from  the  above 
that  the  total  number  of  lines  of  force  cut  by  the  conductor 
is  given  by  the  formula 

N=^  LM  sin  p°.  (474.) 

With  given  values  of  B,  L,  and  M,  it  is  evident  that  iV  is  a 
maximum  when/"  =  90°,  as  then  sin/°  =  1,  and  B  L  J/ sin 
/°  =  B  Z  M^  corresponding  to  the  case  given  in  Art.  301S, 


1902  APPLIED   ELECTRICITY. 

while  if  Z"  =  0°,  then  sin  /°  =  0  and  ^  L  M  sin  /°  =  0, 
which  means  that  if  the  conductor  be  moved  in  a  direction 
at  an  angle  of  0°,  i.  e.,  parallel  to  the  lines  of  force,  no  lines 
will  be  cut  by  it  and  no  E.  M.  F.  generated. 

A  method  of  considering  the  relation  between  the  length 
n  a'  and  the  length  a  a',  which  is  very  useful  in  some  cases, 
is  to  regard  the  length  n  a'  as  the  projection  of  the  length 
a  a'  on  a  plane  at  right  angles  to  the  lines  of  force.  The 
application  of  this  method  will  appear  in  other  parts  of  this 
section. 

3022i.  In  a  similar  manner  other  variations  from  the 
conditions  given  may  be  considered.      Fig.  1125  represents 

^  the  case  where  the  conductor   a    b 

lies  in  a  plane  at  right  angles  to 
the  lines  of  force,  and  is  moved  in 
the  same  plane,  but  in  a  direction 
b  b'  at  an  angle  5,  which  is  not 
a  right  angle,  to  its  length  a  b. 
The  shape  of  the  area  swept  over 
in  moving  from  a  b  to  a'  b'  is  evi- 
dently a  rhomboid,  of  which  the 
area  is  equal  to  the  product  of  the 
base  b  b'  and  the  altitude  a  n.  This 
altitude  being  perpendicular  to  the  base  b  b\  the  triangle 
a  b  n\s  3i  right  triangle,  and,  by  trigonometry,  side  a  n  —.a  b 
sin  s.  Consequently,  the  total  number  of  lines  of  force 
cut  by  the  conductor  a  b  oi  length  L  in  moving  over  a  dis- 
tance b  b'  —  iJ/ through  a  field  whose  density  =  B,  is 

N=E  M Lsms.  (475.) 

Again,  with  given  values  of  B,  L,  and  M,  the  value  of  N 
is  a  maximum  when  s  =  90°,  for  sin  90°  =  1  and  B  if  Z  sin 
s=E  31  L\  and  where  s  =  0°,  sin  s  =  0  and  B  M  L  sin  s  = 
0,  which  means  that  if  the  conductor  is  moved  at  an  angle 
of  0°,  i.  e.,  parallel  to  its  own  length,  no  lines  of  force  are 
cut  by  it,  and  no  E.  M.  F.  is  generated  fn  the  conductor. 

In  this  case,  again,  the  length  a  n  is  the  projection  of  the 


'r-\^r': 

J>;;;-': 

■ '/. ..  '-■..', 
■7  ■..•■.••■/■•■ 

1 

•'.■  •■■,'•■■''''  ' 

Fig. 

1125. 

APPLIED   ELECTRICITY. 


1903 


ttr --—  —  -- 


\i: 


actual  length  of  the  conductor  a  b  om.  plane  at  right  angles 
to  the  direction  of  its  path. 

3023.  Fig.  1126  represents  the  plan  and  elevation  of 
the  case  where  a  conductor  a  b  \s  situated  in  a  magnetic 
field  at  an  angle  r  to  the  lines  of  force,  as 
represented  in  the  elevation,  and  is  moved 
through  the  field  in  the  direction  a  a'  or  b  b' 
at  right  angles  to  the  lines  of  force  and  to 
its  own  length,  as  represented  in  the  plan. 

The  area  swept  over  by  the  conductor  is 
equal  to  the  product  of  its  length  a  b  (see 
elevation)  and  the  length  of  its  path  a  a'  (see 
plan),  but,  as  before,  the  product  of  this  area 
and  the  density  of  the  lines  of  force  is  not 
equal  to  the  total  number  of  lines  of  force 
cut,  as  the  area  is  not  measured  at  right 
angles  to  the  lines  of  force. 

The  number  of  lines  of  force  cut,  how- 
ever, is  measured  by  the  product  of  the  %'y'^'':''':'''''-':''^ 
density,  the  length  of  the  path  of  the  con-  -i-:.:  ' .\:.:^:.:,::.:v^^k\ 
ductor,  and  th.Q  projection  of  its  length  on  a  pie.  nae. 

plane  at  right  angles  to  the  lines  of  force.  This  projection 
is  represented  by  an,  Fig.  1126,  and  the  triangle  a  b  ii  being 
a  right  triangle,  side  a  n  —  a  b  sin  r,  as  before,  and  the  total 
number  of  lines  cut  is 

iV=BJ/Zsinr.  (476.) 

With  given  values  of  B,  Z,  and  M,  N  will  again  have  a 
maximum  value  when  r  =  90°,  as  sin  90°  =  1  and  E  M  L  sin 
r=S  L  M;  and  when  r  =  0°,  and  sin  r  =  0,  B  M  L  sin 
r  =  0,  which  means  that  if  the  conductor  is  located  in  a 
plane  at  an  angle  of  0°,  i.  e.,  parallel  to  the  lines  of  force, 
no  lines  of  force  will  be  cut;  hence,  no  E.  M,  F.  will  be 
generated  by  a  movement  of  the  conductor. 

3024.  For  any  case  where  the  conditions  governing  the 
motions  of  the  conductor  differ  in  more  than  one  re- 
spect from  those   given  in  Art.  3018,  a  formula  may  be 


1904  APPLIED    ELECTRICITY. 

constructed  by  combining  formulas  474,  475,  and  476. 

Thus,  the  total  lines  of  force  cut  by  any  conductor  of  length 
L  situated  in  a  uniform  magnetic  field  of  density  B,  lying 
in  a  plane  at  an  angle  of  r°  with  the  lines  of  force,  and 
moved  with  a  velocity  M  through  the  field  in  a  direction 
at  an  angle  of  s°  with  its  length,  and  at  an  angle  of /°  with 
the  lines  of  force,  will  be  given  by  the  formula  yV=  B  Z  sin 
r°  sin  s°  M  sin  /°,  and  the  E.  M.  F.  resulting  from  this 
motion  will  be  given  by  the  formula 


B  L  sin  r°  sin  s°  M  sin  p" 
10^ 


(477.) 


It  is  evident  that  with  given  values  of  B,  Z,  and  J/,  the 
value  of  N^  hence  of  E^  will  be  a  maximum  when  the  angles 
r,  i",  2in^  p  are  each  equal  to  90°,  while  if  any  of  these  angles 
is  equal  to  0°,  the  value  of  iVand  E  will  be  0. 

It  follows,  then,  that  to  get  the  maximum  E.  M.  F.  with 
a  given  length  of  conductor,  these  angles  should  all  be  as 
near  90°  as  possible,  which  is  the  case  in  almost  all  dynamos, 
as  will  be  pointed  out. 

3025.  Thus  far  a  field  of  uniform  density  has  been 
assumed;  but  from  the  statements  which  have  been  made 
the  effect  of  variations  in  the  density  of  the  field  may  be 
readily  found. 

It  should  be  remembered  that  as  the  E.  M.  F.  generated 
in  a  moving  conductor  is  proportional  to  the  rate  of  cutting 
lines,  it  is  not  necessary  that  the  conductor  should  actually 
move  over  any  particular  area  in  order  that  an  E.  M.  F.  be 
generated  in  it;  it  is  only  required  that  the  conductor  move 
at  such  a  velocity  that  {/"that  velocity  were  maintained  for 
one  second,  the  conductor  would  cut  a  certain  number  of 
lines  of  force,  as  measured  by  the  area  which  would  be  swept 
over.  This  area  is  obviously  the  same  whether  it  encloses 
lines  of  force  or  not;  so  if  at  any  one  point  in  a  conductor's 
path  the  density  is  known,  the  number  of  lines  of  force  which 
would  be  cut  by  the  conductor  in  moving  over  that  area  if 
the  density  were   uniform   at   its  known   value   would  evi- 


APPLIED   ELECTRICITY.  1905 

dently  be  the  product  of  the  known  density  and  the  area, 
and  the  E.  M.  F.  generated  at  the  instant  when  the  con- 
ductor is  passing  through  the  part  of  the  field  where  the 
density  is  of  the  given  value  may  be  found  from  the  for- 
mula. 

3026.  The  considerations  just  mentioned  apply  if  the 
velocity  is  not  constant,  for  if  the  velocity  at  any  instant  is 
known,  the  area  which  would  be  moved  over  by  the  conduct- 
or in  one  second  ?/ the  velocity  were  constant  at  the  known 
value,  measures  the  number  of  lines  which  would  be  cut  in 
one  second,  and  hence  the  rate  of  cutting  or  the  E.  M.  F. 
generated. 

In  actual  practice  the  velocity  of  conductors  in  any  par- 
ticular case  is  almost  invariably  constant,  while  the  density 
of  the  field  is  seldom  uniform. 

Example. — A  conductor  3  feet  3  inches  long  is  dropped  vertically 
through  a  magnetic  field  whose  lines  of  force  are  horizontal,  but  of 
varying  density.  At  a  certain  point  a  the  velocity  is  known  to  be  40 
feet  per  second,  and  at  the  same  point  the  density  of  the  magnetic 
field  is  known  to  be  28,000  dines  of  force  per  square  inch.  What 
E.  M.  F.  is  generated  in  the  conductor  when  at  the  point  a  ? 

Solution. — The  velocity  of  the  conductor  at  this  point  is  40  X  12,  = 

480  in.  per  sec.     The  conductor  being  3  ft.  3  in.  =  39  in.  long,  if  moved 

at  this  velocity  for  one  second  would  sweep  over  an  area  of  480  X  39  = 

18,720  sq.  in.,  which  area  would  enclose  18,720x28,000  =  524,160,000 

lines  of  force,  if  the  density  were  uniform  at  the  known  value  through- 

N 
out  the  area.     From  the  formula  E=^  :-—, 

10** 

„      524,160,000      ^-._      .  . 

E= ^-T--! =  5.241'6  volts.     Ans. 

10** 


THE  EFFECT  OF  CURREIVT   IN  THE   CONDUCTORS. 

3027.     Thus  far,  only  the  production  of  the   E.  M.  F. 

has  been  considered.  If  this  E.  M.  F.  is  allowed  to  act  on 
a  closed  circuit,  so  that  a  current  will  flow,  certain  effects 
will  be  produced,  which  must  be  taken  into  account.  First, 
the  passage  of  the  current  through  the  conductor  implies  a 
loss  or  drop  of  potential  equal  in  value  to  the  product  of 


1906  APPLIED  ELECTRICITY. 

the  current  and  the  resistance  of  the  conductor.  (Art. 
2315.)  The  difference  of  potential  between  the  terminals 
of  the  conductor  in  which  the  E.  M.  F.  is  generated  is  then 
less  than  that  E.  M.  F.,  by  an  amount  equal  to  the  drop. 
Calling  c  the  E.  M.  F.  generated,  or  the  internal  E.  M.  F., 
E  the  difference  of  potential  between  the  terminals,  Ri  the 
internal  resistance  of  the  source  of  ^,  and  C  the  current 
flowing,  then,  E  =■  e  —  C  R,-.  The  total  amount  of  energy- 
expended  in  the  circuit  w  is  evidently  the  product  of  C  and 
e;i.e.,w=zCe.  Of  this,  C  X  C  Ri=  C  Ri  is  expended  within 
the  source  of  the  E.  M.  F.  itself,  leaving  C  e  —  C^  Ri=  C  E  = 
W,  the  energy  expended  in  the  external  circuit,  or  the  otit- 
piit.  It  is  evident  that  as  C^  R^  is  entirely  expended  in 
heating  the  conductors  in  which  the  E.  M.  F.  is  generated, 
it  is  wasted  as  far  as  any  practical  application  is  concerned, 
and  should,  therefore,  be  made  as  small  as  possible,  in  order 
that  C  E  can  be  as  large  a  proportion  as  may  be  of  the  total 
energy  developed,  C  e. 

On  this  account,  the  internal  circuits  of  dynamo  machines 
are  made  of  copper,  that  being  the  metal  which  has  the 
greatest  conductivity  for  a  given  tost  and  bulk. 

3028.  In  addition  to  this  drop  of  potential,  the  pres- 
ence of  the  current  introduces  reactions  between  the  mag- 
netic field  in  which  the  conductors  are  moved  and  the  field 
due  to  tho  current  itself.     (Arts.  2438  and  2439.) 

These  reactions  result  in  a  tendency  for  the  conductor  to 
move,  relative  to  the  lines  of  force  of  the  field,  in  a  direction 
at  right  angles  to  its  own  length  and  to  the  direction  of  the 
lines  of  force. 

The  amount  of  the  force  is  proportional  to  the  amount  of 
current  and  also  to  the  density  of  the  magnetic  field,  meas- 
ured in  a  plane  at  right  angles  to  the  direction  of  the  lines  of 
force.  If  the  length  of  the  conductor  lies  in  this  plane,  the 
force  acting  on  each  centimeter  of  its  length,  when  the  field 
is  of  unit  density  (one  line  of  force  per  square  centimeter) 
and  a  current  of  one  absolute  (C.  G.  S.)  unit  is  flowing 
through  it,  is  one  dyne.     From  this  it  follows  that,  calling 


APPLIED   ELECTRICITY.  1907 

A  the  current  in  absolute  units,  B  the  density  of  the  field 
in  lines  of  force  per  square  centimeter,  and  L  the  length  of 
the  conductor  that  is  within  the  limits  of  the  field  in  cen- 
timeters, the  force  on  the  whole  conductor  in  dynes, 

/=A  BL  (478.) 

3029.  This  force  acts  in  a  direction  at  right  angles  to 
the  length  of  the  conductor  and  to  the  direction  of  the  lines 
of  force;  it  is  evident,  however,  that /"may  be  resolved  into 
components  in  any  other  direction,  by  a  method  similar  to 
that  used  in  finding  the  E.  M.  F.  generated  in  a  moving 
conductor.  If  this  is  done,  it  will  be  found  that  similar 
results  are  obtained;  namely,  that  the  component  of  the 
force/" in  any  direction  is  equal  to  the  value  of  /"  given  by 
the  above  formula  multiplied  by  the  sines  of  the  angles 
which  the  direction  of  the  component  makes  both  with  the 
length  of  the  conductor  and  with  the  direction  of  the  lines 
of  force,  and  of  the  angle  which  the  length  of  the  conductor 
makes  with  the  lines  of  force.  From  this  it  follows  that  if 
any  one  of  these  angles  is  equal  to  0°,  the  component  to 
that  direction  is  also  0;  that  is,  there  is  no  tendency  for  the 
conductor  to  move  in  a  direction  parallel  to  its  own  length 
or  parallel  to  the  lines  of  force,  nor  in  any  direction  if  the 
length  of  the  conductor  is  parallel  to  the  lines  of  force. 

It  will  be  seen  that  the  maximum  component  of  the  direc- 
tion of  the  force  is  in  the  same  direction  as  the  motion 
required  to  produce  the  maximum  E.  M.  F.  in  the  con- 
ductor; and,  further,  in  any  other  direction  the  force  is 
reduced  in  the  same  proportion  as  the  E.  M.  F.  would  be  re- 
duced from  the  maximum  by  movement  in  the  same  direction. 

3030.  If,  then,  the  E.  M.  F.  generated  in  a  moving 
conductor  is  allowed  to  cause  a  current  to  flow,  the  reac- 
tion of  the  current  in  the  magnetic  field  will  cause  the  con- 
ductor to  tend  to  move  in  a  direction  opposite  to  its  motion 
in  generating  the  E.  M.  F.  (See  Arts.  2439  and  2440.) 
In  order  to  move  the  conductor,  it  is  necessary,  then,  to 
apply  to  it  a  force  (neglecting  inertia,  friction,  etc.)  equal  to 


1908  APPLIED   ELECTRICITY. 

the  component  of  the  reaction  between  the  current  and  the 
field  that  is  in  the  direction  in  which  the  conductor  is  moved. 

The  product  of  this  force  and  the  distance  through  which 
the  conductor  is  moved  is  evidently  the  mechanical  work 
done  upon  the  conductor;  hence,  the  product  of  the  force 
and  the  distance  through  which  the  conductor  is  moved  in 
unit  time  is  equal  to  the  rate  at  which  energy  is  expended 
in  moving  the  conductor.  In  C.  G.  S.  units,  then,  zu  = 
A  B  L  M,  where  w  is  the  rate  of  doing  work  in  er^s  per  second ; 
y^,  B,  and  Z  have  the  same  values  as  before,  and  J/ is  the 
distance  through  which  the  conductor  is  moved  in  one 
second,  in  centimeters. 

As  10^  ergs  per  second  equal  1  watt,  dividing  both  sides 
of  the  equation  by  10'  gives  the  power  directly  in  watts,  or 

W=  ■.      By  dividing  the  upper  term  of  the  fraction 

by  10,  C,  the  current  in  amperes,  may  be  substituted  for  A, 

J      U       r  1  Ml   .U  J     7T/  CBLM 

and  the  formula  will  then  read  yy  = — -^ 

10' 

Formula  477,  which  gives  the  E.  M.  F.  generated  in  the 

moving  conductor,  may,  on  the  assumption  here  made  that 

the  angles  between  the  path  of  the  conductor  and  its  length, 

and  the  direction  of  the  lines  of  force,  are  all  90°,  be  written 

E  = — J  in  which  B,  L,  and  Af  have  each  the  same  value 

as  in   the  above   formula;  which,  therefore,  may  be  written 

This  means  t/iat  the  work  done  in  moving  a  conductor 
tJiroiigh  a  magnetic  field  [neglecting  friction  and  inertia^  is 
equal  to  the  zvork  done  by  the  resulting  E.  M.  F.  and  curretit; 
which  also  follows  from  the  law  of  conservation  of  energy. 

3031.  From  this  it  will  be  seen  that  it  is  necessary  to 
supply  mechanical  power  to  the  armature  of  a  dynamo  in 
order  that  it  may  supply  a  current,  and  the  manner  in 
which  this  power  is  expended  should  also  be  clear. 

In  commercial  apparatus,  it  is  evident  that  aside  from 
the  power  required  to  move  the  conductors,  an  additional 


APPLIED   ELECTRICITY.  1909 

amount  of  power  must  be  supplied  for  overcoming  the  fric- 
tion and  all  other  sources  of  loss  that  may  exist  in  the 
mechanism  which  is  used  for  moving  the  conductors; 
further,  the  amount  of  electrical  energy  that  appears  in 
the  external  circuit  is  less  than  the  total  energy  generated, 
by  the  amount  expended  in  heating  the  conductors  in 
which  the  E.  M.  F.  is  generated,  as  has  already  been 
pointed  out.  The  ratio  of  the  energy  appearing  in  the 
external  circuit,  or  the  output  of  the  dynamo,  to  the  total 
amount  generated,  is  called  the  electrical  efficiency  of 
the  dynamo;  the  ratio  of  the  output  to  the  input,  the  input 
being  the  total  amount  of  energy  mechanically  applied  to 
the  conductors  to  move  them,  including  all  losses  in  the 
mechanism  used,  is  called  the  commercial  efficiency  of 
the  machine.  Both  values  are  usually  given  in  per  cent,  of 
the  input;  it  is  evident  that  this  percentage  must  be  less 
than  100,  and  in  commercial  machines  it  ranges  from  75^ 
to  95^,  or  higher,  depending  upon  the  size  and  design. 

In  finding  the  efficiency,  both  output  and  input  must  be 
reduced  to  the  same  units. 

3032.  If,  instead  of  mechanically  moving  the  con- 
ductors through  the  magnetic  field,  they  be  located  therein 
with  their  lengths  at  an  angle  to  the  lines  of  force,  and  an 
E.  M.  F.  from  some  external  source  be  applied  to  the  ter- 
minals of  the  conductors,  a  current  will  flow  through  them, 
and  the  reaction  between  the  field  produced  by  the  current 
and  the  field  in  which  it  is  located  will  produce  a  tendency 
of  the  conductors  to  move  relatively  to  the  magnetic  field, 
just  as  when  the  current  is  produced  by  the  E.  M.  F.  gen- 
erated in  the  conductors  themselves.  This  tendency  is 
exerted  in  a  direction  at  right  angles  to  the  lines  of  force 
and  to  the  length  of  the  conductor,  producing  a  force  act- 
ing in  that  direction,  which  may  be  resolved  into  compo- 
nents acting  in  any  other  direction. 

If  the  conductor  be  free  to  move  in  any  direction,  then 
this  force  will  cause  it  to  move,  provided  its  component  in 
that  direction  is  greater  than  0,  and  the  rate  at  which  work 


1910  APPLIED   ELECTRICITY. 

will  be  done  by  the  conductor  in  moving  will  be  equal  to 
the  product  of  the  value  of  the  force  in  the  direction  of 
motion  and  the  distance  moved  in  unit  time,  i.  e.,  the 
velocity.  This  apparatus  is  then  an  electric  motor, 
capable  of  doing  external  mechanical  work. 

3033.  The  motion  of  the  conductors  through  the  field 
under  these  conditions  will  set  up  in  them  an  E,  M.  F. 
which  is  opposite  in  direction  to  the  E.  M.  F.  which  is 
sending  the  current  through  the  conductors.  (See  Arts. 
2439  and  2440.) 

It  is  evident,  then,  that  in  order  to  keep  up  the  strength 
of  the  current  in  the  moving  conductors,  the  E.  M.  F.  ap- 
plied to  their  terminals  must  be  equal  to  the  E.  M.  F.  gen- 
erated, plus  the  drop  or  fall  of  potential  in  the  conductors. 

3034.  It  has  already  been  shown  that  the  energy  repre- 
sented by  the  product  of  the  force  on  the  conductor  and  the 
velocity  of  the  conductor  is  equal  to  the  energy  represented 
by  the  product  of  the  current  flowing  and  the  E.  M.  F. 
generated  by  the  motion  of  the  conductor.  Calling  e  the 
E.  M.  F.  generated  in  the  winding  and  C  the  current  flow- 
ing, as  before,  the  mechanical  work  done  by  the  moving 
conductor  is  e  C.  The  energy  represented  by  C"^  Ri  {R^ 
being  the  internal  resistance  of  the  conductors),  as  in  the 
case  previously  considered,  appears  only  as  heat.  The  sum 
of  these  two,  then,  equals  the  total  amount  of  energy  which 
must  be  put  into  the  apparatus  to  move  the  conductors; 
that  is,.^  C+C  Ri=  B  C,  E  being  the  E.  M.  F.  applied  to 
the  terminals  of  the  winding.  (Compare  this  with  Art. 
3030.) 

3035.  It  appears,  then,  given  a  conductor,  or  several 
conductors,  situated  in  a  magnetic  field,  with  their  lengths 
at  an  angle  to  the  lines  of  force,  that  the  conductors  may  be 
moved  by  the  application  of  a  mechanical  force  so  that  an 
E.  M.  F.  will  be  generated  in  them,  and  this  E.  M.  F.  may 
be  utilized  in  sending  a  current  through  an  external  circuit; 
this  is  the  dynamo,  in  which  the  mephanical  energy  supplied 


APPLIED   ELECTRICITY.  1911 

is  converted  into  electrical  energy.  Or,  an  E.  M.  F.  may 
be  applied  to  the  terminals  of  the  conductors,  causing  a 
current  to  flow  through  them,  which  will  cause  them  to  move 
through  the  field ;  this  is  the  motor,  in  which  the  electrical 
energy  supplied  is  converted  into  mechanical  energy.  It 
will  be  seen  that  precisely  the  same  features  are  required 
for  both  kinds  of  apparatus,  and  the  same  actions  go  on  in 
both,  the  distinction  being  that  what  is  the  oiitpitt  of  one  is 
the  input  of  the  other.  If  the  conductors  had  no  resistance, 
and  there  was  no  friction  or  any  other  loss  in  the  mechanism 
used  to  transmit  the  mechanical  energy  to  or  from  the  con- 
ductors, then  the  input  would  equal  the  output,  and  the 
efficiency  would  be  100^.  This  is  manifestly  impossible,  so 
that  the  input  must  exceed  the  output  by  the  amount  of 
energy  lost  in  heating  the  conductors  and  in  the  mechanism 
used  to  move  the  conductors,  or  that  is  moved  by  the  con- 
ductors; that  is,  the  efficiency  is  ahvays  less  than  100^,  in 
either  dynamos  or  motors,  and  the  various  losses  are  of  the 
same  kind  in  both  cases.  This  subject  will  be  taken  up  more 
in  detail  later. 

The  development  of  the  various  systems  of  armature 
winding  from  the  principles  that  have  been  given  will  now 
be  taken  up. 

GRAPHICAL  REPRESEIVTATIOIV  OF  E.   M.   F.  OR 
CURRENT. 

3036.  The  value  of  the  E.  M.  F,  generated  in  a  mov- 
ing conductor  during  successive  instants  may  be  graphically 
represented  by  a  "curve  "  on  cross-section  paper,  the  method 
usually  adopted  being  to  make  the  ordinates  represent  the 
E.  M.  F.  and  the  abscissas  either  intervals  of  time  or,  what 
usually  amounts  to  the  same  thing,  distances  passed  over  by 
the  conductor.  In  the  case  of  a  conductor  moving  in  a 
straight  line  at  a  constant  velocity  through  a  uniform  mag- 
netic field  of  unlimited  extent,  the  E.  M  F.  generated  at 
any  instant  is  constant,  and  would,  therefore,  be  represented 
by  a  straight  line  parallel  to  the  axis  of  abscissas,  and  at  a 


1912 


APPLIED   ELECTRICITY. 


certain  distance  from  that  axis,  depending  upon  the  value  of 
the  E.  M.  F.  generated  and  the  scale  selected  to  represent 
it.  Thus,  the  graphical  representation  of  the  E.  M.  F. 
generated  in  the  conductor,  as  given  in  the  example  in  Art. 
3018,  would  be  a  straight  line  parallel  to  the  axis  of  ab- 


6 

— J — 

4 

2 

0 

1 

2 

' 

3 

4 

5 

6 

7 

8 

_ 

Seconds 

Fig.  1127. 

scissas  and  at  a  distance  from  it  equal  to  4.5  volts  on  the 
scale  of  the  ordinates,  as  shown  in  Fig.  1127. 

The  direction  of  the  E.  M.  F.  may  be  found  from  the  rule 
given  in  Art.  2442,  the  E.  M.  F.  being  considered  as  hav- 
ing the  direction  in  which  the  current  which  it  would  pro- 
duce is  considered  to  flow. 

By  applying  this  rule,  it  will  be  seen  that  if  either  the 
direction  of  the  lines  of  force  or  the  direction  of  motion  of 
the  conductor  be  reversed,  the  direction  of  the  E.  M.  F.  is 
also  reversed,  but  if  bot]i  be  reversed,  the  direction  of  the 
E.  M.  F.  is  unchanged, 

3037.  If  the  direction  of  the  motion  of  a  moving  con- 
ductor is  instantly  reversed,  but  the  velocity  maintained 
constant,  the  E.  M.  F.  generated  in  that  conductor  will  be 
reversed  in  direction,  but  unchanged  in  value.  In  order  to 
represent  this  condition  graphically,  it  is  necessary  to  make 
some  distinction  whereby  the  change  in  the  direction  of 
the  E.  M.  F.  will  be  indicated.  This  is  done  by  plotting  the 
E.  M.  F,  curve  on  both  sides  of  the  axis  of  the  abscissas; 
assigning  to  one  side  the  values  of  the  E.  M.  F.  when  in 
one  direction,  and  to  the  other  its  values  when  in  the  opposite 


APPLIED   ELECTRICITY. 


1913 


direction,  both  to  the  same  scale.  It  is  customary  to  plot 
the  curve  of  the  E.  M.  F.  or  current  when  in  a  positive  di- 
rection with  respect  to  some  given  part  of  the  circuit  above 
the  axis  of  the  abscissas,  so  that  this  part  of  the  curve  is 
considered  as  -\-  in  direction. 

Thus,  if  the  conductor  giving  the  curve  represented  in 
Fig.  1127  had  been  moved  in  one  direction  for  2  seconds, 
then  instantly  reversed  and  moved  in  the  opposite  direction 


N 


6q^ 


6 

4 

2 

A 

C 

E 

G 

0 

1 

2 

3 

4 

5 

6 

7 

2 

4 

' 

6 

■ 

Time 
Seconds 

Fig.  1128. 

at  the  same  velocity  for  2  seconds,  then  reversed  again  and 
so  on,  the  curve  of  the  E.  M.  F.  would  be  as  represented  in 
Fig.  1128. 

Here  from  A  to  C  the  curve  is  the  same  as  Fig.  1127,  4.5 
volts  in  one  (the  -\-)  direction ;  at  C  (the  end  of  the  2d  second) 
the  direction  of  the  motion,  also. the  E.  M.  F.,  is  reversed, 
and  is  represented  by  the  line  drawn  on  the  other  side  of  the 
axis  of  the  abscissas  from  C  to  E,  where  the  E.  M.  F.  is 
again  reversed,  and  so  on. 

As  at  the  instant  the  E.  M.  F.  is  reversed  it  passes  through 
all  the  intermediate  values  between  4.5  volts  in  one  direc- 
tion and   4.5  volts  in   the   other,  a  line   must  be  drawn   to 


1914 


APPLIED   ELECTRICITY. 


indicate  all  these  values,  as  shown  ;  the  reversal  being 
assumed  to  be  instantaneous,  this  line  coincides  with  the 
ordinate  which  passes  through  the  abscissa  which  represents 
the  time  at  which  the  reversal  took  place,  as  at  2  seconds, 
4  seconds,  6  seconds,  etc. 

3038.  If  the  change  from  the  maximum  E.  M.  F,  in 
one  direction  to  the  maximum  in  the  other  were  not  instan- 
taneous, this  line  would  not  coincide  with  one  of  the  ordi- 
nates;  for  example,  assume  that  this  same  conductor  was 
not  moved  at  a  constant  velocity,  but  with  a  uniform  acceler- 
ation of  such  an  amount  that,  starting  from  zero,  the  velocity 
at  the  end  of  the  1st  second  was  the  same  as  the  constant 
value  assumed  in  the  previous  case ;  then  the  E.  M.  F. 
generated  at  successive  instants  during  this  1st  second 
would   be   represented,  as  in   Fig.  1129,  by   a   straight  line 


6 

# 

1 

\ 

1 

\ 

\ 

\ 

^   / 

1 

\ 

1 

\ 

^■^ 

/ 

\ 

/. 

\ 

C 

t: 

G 

63" 

6 

1 

2 

\ 

3 

1 

4 

•S 

6 

\ 

7 

2 

\ 

1 

\ 

"A 

1 

1 

4 

/ 

1 

/ 

1 

6 

Time 
Seconds 

Fig.  1129. 

commencing  at  0  volts  at  0  time  and  rising  to  4.5  volts  at 
the  end  of  the  1st  second. 

If  from  this  point  the  velocity  of  the  conductor  is  retarded 
at  the  same  rate  as  it  was  previously  accelerated,  its  velocity 
at  the  end  of  the  2d  second  would  be  0  and  the  curve  of  the 


APPLIED   ELECTRICITY. 


1915 


E.  M.  F.  generated  during  the  2d  second  would  again  be  a 
straight  line,  commencing  at  4.5  volts  at  the  end  of  the  1st 
second  and  falling  to  0  volts  at  the  end  of  the  2d  second. 

If  the  conductor  is  now  moved  in  the  opposite  direction 
and  the  same  cycle  of  acceleration  and  retardation  gone 
through  with,  the  curve  of  the  E.  M.  F.  generated  during 
this  cycle  of  motions  will  be  of  exactly  the  same  shape  as 
that  for  the  previous  cycle,  but  will  lie  on  the  opposite  side 
of  the  line,  as  is  represented  by  the  part  C  E  oi  the  curve 
shown  in  Fig.  1129.  Continuation  of  this  cycis  of  motion 
gives  a  series  of  repetitions  of  this  curve,  as  represented  in 
Fig.  1129. 

3039.  A  similar  curve  would  result  if  the  velocity  of 
the  conductor  had  been  kept  constant,  as  in  the  case  in  Art. 
3037",  but  the  density  of  the  field  had  been  uniformly 
varied  along  the  path  of  the  conductor  from  0  to  a  maximum, 
and  then  to  0  again. 

Both  of  these  cases  assume  that  the  change  from  acceler- 
ating to  diminishing  velocity,  or  from  increasing  to  decreas- 
ing density,  is  instantaneous,  as  indicated  by  the  sharp  peaks 
of  the  E.  M.  F.  curve.  In  any  apparatus  as  actually  con- 
structed these  changes  would  be  more  gradual,  which  would 
result  in  more  or  less  rounding  the  peaks  of  the  curve. 

3040.  If  a  conductor  is  moved  in  a  straight  line  through 
a  succession  of  magnetic  fields  of  alternate  polarity,  as  rep- 
resented in  Fig.  1130,  the  curve  of  the  E.  M.  F.  generated 


Pig.  1130. 
will  be  of  similar  character  to  those  shown  in  Figs.  1128  and 
1129;  that  is,  the  E.  M.  F.  will  be  maintained  in  one  direc- 
tion as  long  as  the  conductor  is  moving  through  a  field  of 


1916 


APPLIED   ELECTRICITY. 


one  polarity,  but  as  soon  as  the  direction  of  the  lines  of 
force  is  reversed,  the  E.  M.  F.  is  also  reversed  .  (Art.  ,3036.) 
The  actual  shape  of  the  waves  of  the  curve  will  depend,  as 
in  the  previous  cases,  upon  the  variation  in  the  uniformity 
of  the  density  of  the  field  or  of  the  velocity. 

The  manner  of  finding  the  E.  M.  F.  generated  in  any 
conductor  moved  in  any  straight  line  through  a  magnetic 
field  of  any  condition  of  density  should  now  be  clear. 

It  is  evident,  however,  that  motion  in  a  straight  line  or 
in  any  irregular  line  is  not  in  general  desirable  for  dynamos; 
motion  in  a  straight  line  can  not  be  indefinitely  continued, 
for  that  would  require  a  field  of  unlimited  extent,  and  sud- 
den changes  in  the  direction  of  motion  of  the  conductor  do 
not  usually  permit  of  good  mechanical  construction.  To 
avoid  both  the  infinite  field  and  the  sudden  changes  in  the 
direction  of  motion,  the  conductor  may  be  moved  in  a  circu- 
lar path,  which  is  mechanically  convenient  and  allows  of 
the  use  of  a  field  of  limited  extent;  the  effect  of  such  motion 
will  now  be  considered. 


3041.  In  the  case  of  a  conductor  moving  in  a  circular 
path  through  a  field  of  uniform  density,  if  the  lines  of  force 
are  at  every  point  radial  to  the  path  of  the  conductor,  as 
represented  in  Fig.  1131,  the  angle  which  the  direction  of 

motion  of  the  conductor 
makes  with  the  lines  of 
force  at  every  instant  is 
constant;  the  E.  M.  F. 
generated  in  the  con- 
ductor is,  therefore,  con- 
stant as  long  as  a  constant 
velocity  is  maintained. 

In  order  to  obtain  the 
distribution  of  the  lines  of 
force  required  in  the 
above  case,  one  pole  of 
the  magnet  i^S  S  S  S) 
Fig.  iiai.  must  be  made  in  the  form 


APPLIED   ELECTRICITY.. 


1917 


of  a  hollow  cylinder,  concentric  with  and  enclosing  the  path 
of  the  conductor  {a  n  a')  and  the  other  pole  [N  N JVN).  In 
the  space  between  these  two  poles  the  lines  of  force  will  be 
radial  in  direction  and  uniform  in  density  if  the  rest  of  the 
magnetic  circuit  is  properly  designed. 

3042.  If  the  direction  of  the  length  of  the  conductor 
is  radial,  instead  of  parallel  to  the  axis,  as  in  the  above  case, 
by    making    the    lines    of    force 
parallel  to  the  axis  and  uniform 
in   density  all  along  the   path  of 
the  conductor,  the  angle  between 
the   lines  of  force  and  the  direc- 
tion of  motion  of  the   conductor 
will  at  all  instants  be  the  same; 
hence,  the  E.  M.  F.  will  be  of  the 
same  character  as  before.     This 
arrangement  of  the  lines  of  force 
may  be  obtained   by   making  the 
pole  faces  circular   in   shape  and 
placing     them     in     two    parallel  r'- 
planes    with    the    center    of    the  i  ' 
pole-pieces    coinciding    with    the                    ^'°-  ^^^^• 

axis  of  rotation  of  the  conductor,  as  represented  in  Fig.  1132. 
The  arrangement  of  the  balance  of  the  magnetic  circuit 
is  not  indicated  in  this  figure.  A  part  of  the  north  pole- 
piece  is  broken  away  in  the  elevation  to  show  the  con- 
ductor a  0.  

THE  SINE  CURVE. 

3043.  Fig.  1133  illustrates  a  case  of  circular  motion 
which  differs  in  many  features  from  the  first  two  considered. 
Here  the  lines  of  force  are  parallel  to  each  other  and  at 
right  angles  to  the  axis  of  rotation;  consequently,  the  angle 
between  the  direction  of  motion  and  the  direction  of  the 
lines  of  force  changes  at  every  instant.  From  this  it  fol- 
lows that  the  E.  M.  F.  also  varies  during  successive  in. 
stants.  Although  the  direction  of  motion  of  the  conductor 
changes,  at  any  one  point  it  may  be  considered  to  be  along 


1918 


APPLIED   ELECTRICITY. 


a  straight  line  tangent  to  the  circle  at  that  point,  and  a  cer- 
tain length  may  be  assigned 
to  this  line  which  will  represent 
the  velocity  of  the  moving  con- 
ductor. Thus,  at  the  instant 
when  the  conductor  is  at  the 
point  a  (Fig.  1133)  of  its  path, 
the  line  representing  its  direc- 
tion of  motion  at  that  point 
makes  an  angle  of  0°  (is  par- 
allel) with  the  lines  of  force; 
hence,  no  E.  M.  F,  is  generated 
at  this  point.  As  the  conduct- 
or moves  along  its  path,  this 
angle  becomes  greater  until  at 
a  point  90°  from  a  the  angle  is 
also  90°,  and  the  E.  M.  F.  gen- 
erated is  a  maximum.  Further 
Fig.  1133.  continuation  of  the  motion  for 

another  90°  decreases  the  angle  until  it  is  again  0°,  and  the 
E.  M.  F.  is  again  zero. 

The  remainder  of  the  revolution  repeats  this  cycle  of 
changes  of  the  angle,  but,  as  the  conductor  is  moving  in 
the  opposite  direction  relative  to  the  lines  of  force,  the 
E.  M.  F.  is  reversed  in  direction.  From  this  it  follows  that 
the  curve  of  this  E.  M.  F.  would  form  a  series  of  waves  on 
each  side  of  the  axis  of  the  abscissas,  as  in  the  cases  de- 
scribed in  Arts.  3037  and  3038. 


3044.  The  shape  of  the  waves  of  this  curve  may  be 
found  by  calculating  the  E.  M.  F.  generated  at  successive 
intervals  of  time;  this  E.  M.  F.  will  evidently  be  propor- 
tional to  the  sine  of  the  angle  which  the  direction  of  motion 
makes  with  the  lines  of  force  (see  Art.  3020),  so  that  by 
constructing  at  any  point  on  the  circle  a  right-angled  tri- 
angle which  includes  the  above  angle,  the  side  opposite  this 
angle  may  be  used  as  the  length  of  the  ordinate  represent- 
ing the  E.  M.  F.  generated  at  that  point. 


APPLIED   ELECTRICITY. 


1919 


This  process  is  represented  in  Fig.  1134,  where  b  repre- 
sents a  certain  point  in  the  path  of  the  conductor  a  at  which 
it  is  desired  to  know  the  E.  M. 
F.  generated.  The  line  h  r, 
tangent  to  the  circle  at  the 
point  b,  represents  the  direc- 
tion of  the  motion  of  the  con- 
ductor at  this  point,  and  makes 
the  angle  /  with  the  direction 
of  the  lines  of  force,  repre- 
sented by  the  line  ?'  t.  The 
line  /  b,  at  right  angles  to  r  t, 
is,  then,  the  sine  of  the  angle/; 
hence,  it  is  a  measure  of  the 
E.  M.  F.  generated  in  the  con- 
ductor at  the  point  b,  and  by 
repeating  this  process  for  suc- 
cessive points  around  the  circle 
a  series  of  values  will  be  ob- 
tained which  may  be  used  as 
ordinates  of  the  E.  M.  F.  curve,  as  stated. 

From  the  construction  of  the  figure,  the  line  o  b  \s  per- 
pendicular to  the  line  b  r,  and  the  line  o  a  is  perpendicular 
to  the  line  r  t;  hence,  the  angle  d  included  between  the 
lines  0  a  and  ^  ^  is  equal  to  the  angle  /  included  between 
the  lines  b  r  and  r  t,  and  the  E.  M,  F.  is,  therefore,  propor- 
tional to  the  sine  of  the  angle  d,  or  to  the  length  of  the  line 
b  n.  This  length  {b  li)  may  or  may  not  equal  the  E.  M.  F. 
when  laid  out  on  any  scale,  but  will  always  be  proportional 
to  it. 

Hence,  the  E.  M.  F.  generated  at  any  instant  in  a  con- 
ductor moving  in  a  circular  path  through  a  magnetic  field 
of  uniform  density  whose  lines  of  force  are  at  right  angles 
to  the  axis  of  rotation  and  parallel  to  each  other  is  propor- 
tional to  the  sine  of  the  angle  through  whicJi  the  conductor 
has  been  rotated  from  a  point  where  its  direction  of  motion  is 
parallel  to  the  lines  of  force. 


Fig.  1134. 


[920 


APPLIED  ELECTRICITY. 


3045.  If  the  velocity  of  the  conductor  is  uniform  (as  is 
assumed  above),  the  conductor  will  move  through  equal 
angles  in  equal  intervals  of  time;  hence,  the  abscissas  of  the 
E.  M.  F.  curve  may  represent  either  the  intervals  of  time 
required  for  the  conductor  to  move  through  the  various 
angles  or  the  angles  themselves.  The  ordinates  may  repre- 
sent the  sines  of  the  same  angles,  the  E.  M.  F.  being  pro- 
portional to  them.  This  curve  may  be  conveniently  drawn 
by  laying  off  on  a  circle  a  series  of  points  representing  suc- 
cessive positions  of  the  conductor  after  equal  intervals  of 
time,  as  represented  at  «,  /^,  ^,  .  .  .  .  a'  in  Fig.  1135   {a)^ 


45°       90^     laS"     180 
or  Angle  in  Degrees 


a  a'  being  a  diameter  at  right  angles  to  the  lines  of  force. 
The  vertical  height  of  any  of  these  points  above  the  diameter 
a  a!  is,  then,  the  sine  of  the  angle  through  which  the  conduct- 
or has  been  moved,  and  these  heights  may  be  projected  on 
the  ordinates  of  properly  arranged  cross-section  paper,  as 
represented  in  Fig.  1135  (^),  giving  the  curve  a,  b,  c^  .  .  .  . 
a\  as  shown.  The  curve  for  the  remainder  of  the  revolu- 
tion, a'  in  a,  may  be  laid  out  in  the  same  way,  and  would  evi- 
dently be  of  the  same  shape,  but  would  be  on  the  opposite 
side  of  the  axis  of  the  abscissas.  This  form  of  curve  is 
called  a  sine  curve,  or  sinusoid,  from   its  method  of  con- 


APPLIED   ELECTRICITY.  1921 

struction,  and  possesses  several  peculiar  features,  as  will  be 
pointed  out. 

3046.  Value  of  E.  M.  F. — From  the  explanation 
given  in  Art.  3024,  it  will  be  seen  that  the  E.  M.  F.  gen- 
erated in  the  conductor  in  the  above  case  at  any  instant  may- 
be found  from  formula  477  ;  r°  and  s°  being  in  thi&  ease 
each  equal  to  90°,  sin  r°  and  sin  s°  are  each  equal  to  ),  and 
may  be  omitted,  making  the  formula  read 

^_  BZJ/sin  /" 
10^' 

It  is  evident  that  during  one  complete  revolution  the  con- 
ductor passes  over  a  distance  equal  to  2  tt  r,  r  being  the 
radius  of  its  circular  path,  or  o  a  (Fig.  1135). 

Then,  if  the  speed  of  the  conductor  is  vS  revolutions  per 

S  /  S 

minute,  its  velocity  is  equal  to  ^^^^(T^^^i^g  the  revolu- 
tions per  second),  and  this  value  may  be  substituted  for  M' 
in  the  above  formula,  which  would  then  read 

BZ  27rr--sin/° 
j^  dO 

£=  — 


10" 

All  the  lines  of  force  cut  by  the  conductor  in  each  revolu- 
tion are  included  in  the  area  obtained  by  multiplying  to- 
gether L  and  2  ?'.  This  being  the  case,  the  total  numbei  of 
lines  cut  by  the  conductor,  which  is  represented  by  A^,  is 
equal  to  B  Z.  2  r. 

N 
From  this,  — -  =  B  L,  which  value  may  be  substituted  for 

2  r  ■' 

BZ  in  the  previous  formula,  which  then  reads  as  follows: 

N  S 

^_27'"^60^^^^° 
^  "  10" 

Simplifying  this,  it  becomes 

^  ~     10*  X  60   • 


1922 


APPLIED   ELECTRICITY. 


When  E  is  at  its  maximum  value,  ^,„,  ^°  ;=  90°  and  sin/°  =  1 ; 
hence, 

^-  =  i#i4o-  (479.) 


THE    AIR-GAP. 

3047.  If  the  field  through  which  the  conductor  moves 
in  its  circular  path,  having  a  radius  o  a,  exists  between  two 
parallel  pole  faces,  as  represented  in  Fig.  1135,  it  is  evident 
that  the  distance  between  the  pole  faces  must  be  a  little 
greater  than  2  ^  «,  in  order  that  the  conductor  may  not  touch 
the  pole  faces  in  its  rotation. 

This  distance  between  the  pole  faces  introduces  an  air-gap 
of  great  length  compared  to  its  area,  thus  requiring  a  con- 
siderable expenditure  of  M.  M.  F.  (magnetomotive  force) 
in  forcing  the  field  across  the  gap. 

The  average  length  of  this  air-gap  may  be  reduced  by 
making  the  pole  faces  concentric  with  the  path  of  the  con- 
ductor, but  as  in  this  case  the  length  of  the  air-gap  is  no 
longer  uniform,  the  density  of  the  field'  in  the  gap  will  not 
be  uniform;  and,  further,  the  increased  density  is  situated 

at  a  point  where  it  has  the  least 
effect;  i.  e.,  at  the  point  where 
the  conductor  is  moving  in  a 
direction  nearly  or  quite  parallel 
to  the  lines  of  force,  as  repre- 
sented in  Fig.  1136. 

3048.  As  there  is  actually 
required  for  the  movement  of 
the  conductor  only  a  thin  cyl- 
indrical space  near  the  pole 
faces,  the  length  of  the  air-gap 
may  be  reduced  very  largely  by 
filling  in  the  space  not  required 
for  the  movement  of  the  con- 
FiG.  1136.  ductor  with  a  cylindrical  core  of 

iron.     The   distribution   of    the  lines  of   force  will  now  be 


APPLIED   ELECTRICITY. 


1923 


materially  different  from  that  shown  in  Fig.  1136;  the 
length  of  the  air-gap  being  practically  uniform  and  much 
shorter,  the  direction  of  the  lines  of  force  will  be  in  nearly 
the  shortest  distance  across  the  gap,  i.e.,  will  be  nearly 
radial,  and  the  density  will  be  practically  uniform  and,  with 
the  same  M.  M.  F.,  much  higher. 

The  actual  distribution  of  the  lines  of  force  will  be  about 
as  represented  in  Fig. 
1137.  It  will  be  noted 
that  some  of  the  lines 
of  force  do  not  pass  into 
the  core  at  all,  and  are 
even  entirely  outside 
the  path  of  the  con- 
ductor. These  leakage 
lines  (see  Art.  2415) 
are  always  present  in 
any  magnetic  circuit 
which  includes  an  air- 
gap,  although  they  have 
not  thus  far  been  repre- 
sented. Their  influence  fig.  1137. 
on  the  design  of  the  magnetic  circuit  may  be  neglected 
for  the  present,  but  will  be  fully  discussed  later. 


3049.  If  the  lines  of  force  in  the  air-gap  were  abso- 
lutely radial  and  of  uniform  density  throughout,  the  direc- 
tion of  the  motion  of  a  conductor  moving  through  this  air- 
gap  would  at  any  instant  be  at  right  angles  to  the  lines  of 
force,  and  (assuming  a  constant  velocity)  the  E.  M.  F. 
would  be  constant  in  value,  but,  of  course,  reversed  at  the 
end  of  each  half  revolution.  The  E.  M.  F.  curve  would, 
therefore,  be  similar  to  that  shown  in  Fig.  1128,  Art.  3037. 

This  differs  from  the  case  described  in  Art.  3041,in  that 
the  direction  of  the  motion  of  the  conductor  with  respect  to 
the  direction  of  the  lines  of  force  is  not  constant,  but  is  re- 
versed at  the  end  of  each  half  of  a  revolution,  which  causes 
the  E.  M.  F.  to  be  reversed,  as  stated- 


1924  APPLIED   ELECTRICITY. 

The  actual  distribution  of  the  lines  being  different  from 
this  just  described,  the  curve  is  actually  more  like  the  sine 
curve  (Fig.  1135),  but  with  a  more  flattened  top,  conse- 
quently a  more  rapid  increase  from  zero  to  values  near  the 
maximum. 

ARMATURE    CORE    LOSSES. 

3050.  A  very  convenient  method  of  moving  the  con- 
ductor through  the  magnetic  field  is  to  mechanically  attach 
it  to  the  surface  of  the  cylindrical  core,  which  may  then  be 
rotated  around  its  axis  by  any  convenient  means.  The 
motion  of  the  core  does  not  of  itself  affect  the  distribution 
or  the  density  of  the  lines  of  force  ;  but  in  order  to  maintain 
the  motion  of  the  core,  certain  losses,  due  to  hysteresis  and 
to  eddy  currents  circulating  in  the  core,  must  be  overcome. 

3051.  The  hysteresis  is  due  to  the  continual  change  in 
the  direction  of  the  lines  of  force  through  the  core,  as  it 
rotates,  amounting  to  one  complete  reversal  in  each  half 
revolution  ;  the  amount  of  the  hysteresis  loss  depends  upon 
the  quality  of  the  iron  of  which  the  core  is  made,  the  density 
of  the  lines  of  force  in  the  core,  the  number  of  reversals  of 
magnetism  per  unit  of  time,  and  the  amount  of  iron  affected. 
(Art.  2413.) 

3052.  The  eddy-current  loss  is  due  to  the  fact  that, 
the  iron  of  the  core  being  a  conductor,  the  E.  M.  F.  gen- 
erated in  it  by  its  rotation  in  the  magnetic  field  causes  cur- 
rents to  circulate  through  the  mass  of  metal  in  the  core  ; 
these  currents  do  not  differ  from  the  currents  flowing  in  the 
conductors  attached  to  the  surface  of  the  core,  but  as  they 
do  not  appear  in  the  external  circuit,  they  represent  so  much 
wasted  energy. 

3053.  The  E.  M.  F.  of  these  eddy  currents  is  neces- 
sarily low  ;  but  if  the  core  is  a  solid  mass  of  metal,  the  re- 
sistance offered  to  these  currents  is  extremely  small,  so  that 
the  small  E.  M.  F.  may  cause  enormous  currents  to  flow, 
which  would  thereby  be  the  source  of  a  great  loss  of  energy. 


APPLIED   ELECTRICITY. 


1925 


The  direction  of  these  currents  may  be  found  by  applying 
the  rule  given  in  Art.  2442,  when  it  will  be  seen  that  if 
the  direction  of  the  current  in  a  section  of  the  core  under 
one  pole  is  from  front  to  back,  under  the  other  pole  it 
will  be  from  back  to  front,  so  that  these  currents  will  circu- 
late around  the  core,  as  represented  in  Fig.  1138,  in  which 
only  the  lower  half  of  the  core  is  represented,  the  paths  of 
the  eddy  currents  being  indicated  by  the  lines  with  the 
arrow-heads. 

In  order  to  reduce  the  value  of  the  eddy  currents  as  much 
as  possible,  it  is  evidently 
necessary  to  reduce  their 
E.  M.  F.  and  to  increase 
the  resistance  of  their  path. 
This  is  usually  accomplished 
by  building  up  the  core  of 
a  number  of  thin  iron  disks, 
as  represented  in  Fig.  1139, 
arranged  parallel  to  the 
lines  of  force  and  at  right  fig.  iiss. 

angles  to  the  axis  of  rotation,  and  insulated  from  one 
another. 

Instead  of  being  one  single  conductor  of  large  section, 

the  core  is  now  made 
up  of  a  number  of 
conductors  of  less 
section  and  shorter 
length  ;  the  E.  M.  F. 
generated  in  each 
conductor  is,  there- 
fore, much  less,  and 
the  current  produced 
Fig.  1139.  thereby  is  relatively 

much  smaller  than  in  the  case  of  the  solid  core,  so  that  the 
loss  of  energy  is  reduced. 


3054.     This  process  of  dividing  the  core  into  thin  plane 
sections  is  called  lamination,  the  separate  sections  forming 


1926 


APPLIED   ELECTRICITY. 


the  laminae.  Lamination  does  not  affect  the  magnetic 
qualities  of  the  core,  since  all  the  sections  are  continuous  in 
the  direction  of  the  lines  of  force. 

,  Building  up  the  core  of  lightly  insulated  iron  wire  will 
also  prevent  eddy  currents,  but  as  in  this  case  the  iron  of 
the  core  is  not  magnetically  continuous,  the  reluctance  of 
the  core  as  a  whole  is  much  greater  than  that  of  the  iron  of 
which  it  is  composed.  The  laminated  structure  is,  there- 
fore, most  extensively  used. 

3055.  As  in  the  case  mentioned  in  Art.  3042,  the 
direction  of  the  length  of  the  conductor  may  be  radial 
instead  of  parallel  to  the  axis  of  rotation.  In  that  case 
the  cylindrical  core  would  take  the  form  of  a  disk,  and  the 
lines  of  force  would  enter  and  leave  the  core  at  the  end  faces 
instead  of  the  cylindrical  face,  as  represented  in  Fig.  1140, 
a  h  being  the  conductor  supported  on  the  core  C,  which 
rotates  about  the  axis  o  o' . 


Fig.  1140. 

The  curve  of  the  E.  M.  F.  generated  under  these  circum- 
stances would  be  similar  to  that  mentioned  in  Art.  3049, 
i.  e.,  similar  to  a  sine  curve,  but  with  flatter  peaks  to  the 
waves. 

From  an  inspection  of  the  figure,  it  will  be  seen  that  if  the 
core  were  made  up  of  disks  arranged  at  right  angles  to  the 
axis  of  rotation  as  in  the  previous  case,  the  laminae  would  not 
act  to  reduce  the  B.  M.  F.  available  for  the  production  oi 


APPLIED   ELECTRICITY.  1927 

eddy  currents;  so  this  type  of  core  is  usually  constructed  of 
a  long  strip  of  thin  iron,  wound  in  a  helical  form,  with  strips 
of  insulating  material  between  the  layers.  This  makes  a 
core  of  the  requisite  form  that  is  magnetically  continuous 
in  the  direction  of  r.he  lines  of  force,  and  is  free  from  excessive 
eddy  currents. 


CHARACTER    OF    COMMERCIAL    CURRENTS. 

3056.  Any  electric  current  in  commercial  use  may  be 
classified  either  as  a  direct  current  or  an  alternating 

current.  The  abbreviations  for  these  are  D.  C,  direct  cur- 
rent, and  A.  C,  alternating  current. 

A  direct  current  may  be  defined  as  a  current  which  ahvays 
flozvs  in  the  same  direction  through  the  conductor  or  circuit. 

A  direct  current  may  be  continuous,  so-called,  or  pul- 
sating. A  strictly  continuous  current  is  one  in  which  the 
E.  M.  F.  has  an  absolutely  constant  value  during  succeeding 
intervals  of  time,  which  would,  therefore,  cause  a  perfectly 
steady  current  to  flow  through  a  circuit  of  constant  resist- 
ance. 

The  curve  of  a  continuous  current  would  then  be  a  straight 
line  parallel  to  the  axis  of  the  abscissas,  as  represented  in 
Fig.  1127.  Incandescent  dynamos  or  constant  potential 
dynamos  are  familiar  examples  of  machines  that  furnish 
continuous  currents. 

3057.  The  pulsating  current  is  practically  unknown  in 
the  commercial  world,  and  although  the  current  from  a 
Thomson-Houston  arc  machine  may  be  called  a  pulsating 
current,  yet  it  is  never  mentioned  as  such.  As  will  be 
explained  farther  on,  a  pulsating  current  is  one  which 
always  flows  in  the  same  direction,  but  the  electromotive 
force  constantly  varies,  so  that  the  current  consists  of  dis- 
tinct impulses  or  rushes  of  current. 

In  Fig.  1141,  {a),  {b),  and  {c)  represent  three  possible  curves 
of  pulsating  currents;  in  {a)  the  fluctuations  of  the  E.  M.  F, 
or  current  occur  between  a  m^ximurn  and  zero,  while  in  {^b) 


1928 


APPLIED   ELECTRICITY. 


the  minimum  is  about  .7  of  the  maximum;  {c)   represents 

a  slightly  different  type  of 
curve,  in  which  the  mini- 
mum is  about  .85  of  the  maxi- 
mum. It  will  be  seen  that 
either  of  the  last  two  quite 
closely  approaches  a  strictly 
continuous  current. 


^ 


f 

N 

/■ 

"^ 

^ 

N 

r 

N  . 

J 

V 

I 

J 

I 

J 

0   Time 


(a) 


1 

^ 

N 

\^ 

/ 

^ 

^ 

\ 

y 

^ 

1 

Time 


(b> 


^ 


0     Time 


3058.  An  alternating 
current  may  be  defined  as  a 
current  which  is  continually 
reversed  in  direction;  conse- 
quently, its  E.  M.  F,  and 
current  alternate  between 
two  opposite  maximum  val- 
ues; the  curve  of  the  E.  M. 
F.  or  current  would,  there- 
fore, lie  on  both  sides  of  the 
^(.^  axis  of  the  abscissas.     A  dy- 

FiG.  1141.  namo  which  generates  an  al- 

ternating E.  M.  F.  is  called  an  alternator.  The  E.  M.  F. 
generated  in  a  conductor  whose  direction  of  motion  with 
respect  to  the  direction  of  the  lines  of  force  is  periodically 
reversed  would,  therefore,  be  an  alternating  E.  M.  F.,  as 
shown  by  the  curves  in  Figs.  1128,  1129,  and  1135. 

If  the  conductor  so  moved  cuts  the  lines  of  force  in  each 
direction  in  the  same  time  and  at  the  same  rate,  the  curves 
of  the  E.  M.  F.  generated  by  the  motion  in  each  direction 
will  both  be  of  the  same  shape,  and  will  lie  equally  on  both 
sides  of  the  axis  of  the  abscissas,  and  a  continuation  of  the 


F 

/ 

\ 

/ 

\ 

/ 

\ 

A 

V 

V 

y 

E 

O 

V 

/ 

1 

K 

V 

y 

M 

K 

1 

"ijwe 

Fig.  1148. 


cycle  of  motions,  under  the  same  conditions,  will  give  an 
E.  M.  F.  curve  that  is  merely  a  series  of  repetitions  of  the 


APPLIED   ELECTRICITY.  1929 

curve  representing  the  E.  M,.  F.  generated  during  the  first 
cycle  of  motions.  Such  an  E.  M.  F.  (or  its  resulting  cur- 
rent) is  called  a  cyclic,  periodic,  or  tiarmonic  alternating 
E.  M.  F.  (or  current).  A  curve  showing  a  form  of  such  an 
E.  M.  F.  is  given  in  Fig.  1142,  the  axis  being  A  M;  the 
positive  impulses  are  above,  at  V,  and  the  negative  impulses 
at  JC.     The  curve  crosses  the  axis  at  the  points  C,  B,  G,  etc. 


GENERAL   PRIIVCIPLES    OF    ARMATURE 
WINDINGS. 

3059.  It  should  be  clear  that  rotary  motion  of  a  con- 
ductor in  a  magnetic  field  may  be  divided  into  two  gen- 
eral classes:  (1)  where  the  arrangement  of  the  field  with 
regard  to  the  path  of  the  conductor  is  such  that  the  direc- 
tion of  the  motion  is  always  the  same,  relative  to  the  direc- 
tion of  the  lines  of  force,  and  (2)  where  the  arrangement  is 
such  that  the  direction  of  motion  is  periodically  reversed, 
relative  to  the  direction  of  the  lines  of  force. 

A  further  distinction  between  these  two  classes  is  that  in 
the  first  class  each  line  of  force  is  cut  oily  once  in  each  rev- 
olution, while  in  the  second  class  each  line  of  force  is  cut 
twice  in  each  revolution.  This  has  given  rise  to  the  names 
unipolar  and  bipolar  (or  multipolar)  induction  for  the 
two  classes;  i.  e.,  the  E.  M.  F.  generated  in  a  conductor  so 
arranged  as  to  come  under  the  first  class  would  be  said  to 
be  due  to  iinipolar  induction,  etc.  These  terms  have  been 
extended  to  the  machines  themselves,  so  a  machine  in 
which  the  E.  M.  F.  is  generated  by  unipolar  induction  is 
called  an  unipolar  dynaino;  if  the  E.  M.  F.  is  generated  by 
bipolar  induction,  it  is  called  a  bipolar  dynamo,  and  so  on. 
This  application  of  the  term  tcnipolar  is  hardly  correct, 
since  an  "unipolar  dynamo"  must  necessarily  have  two 
poles.  Its  application  to  induction,  however,  is  more  accu- 
rate, because,  aside  from  its  influence  on  the  design  of  the 
magnetic  circuit,  the  presence  of  more  than  one  pole  is  not 
necessary  in  considering  this  class  of  induction;  that  is,  as 


1930  APPLIED   ELECTRICITY. 

each  line  of  force  is  cut  only  at  one  point,  it  does  not  mat- 
ter what  course  it  takes  after  being  cut.  With  bipolar  or 
multipolar  induction,  it  is  necessary  that  the  lines  from 
each  magnet  be  grouped  together  in  the  same  manner  at 
the  two  separate  points  of  their  own  path  at  which  they  are 
cut  by  the  conductor,  which  is  most  conveniently  done  by 
making  these  points  the  surfaces  of  the  poles  of  the  magnet. 
Still,  the  distinction  is  usually  applied  to  the  machines 
themselves. 

3060.  It  has  been  shown  that  with  either  unipolar  or 
bipolar  induction  the  conductor  may  occupy  one  of  two 
radically  different  positions;  namely,  the  direction  of  its 
length  may  be  parallel  or  radial  to  the  axis  of  rotation. 
In  either  case,  with  unipolar  induction,  as  illustrated  in 
Arts.  3041  and  3042,  Figs.  1131  and  1132,  it  is  evident 
that  the  E.  M.  F.  generated  in  the  conductor  is  a  direct 
E.  M.  F.  in  the  sense  of  being  continuous  in  direction,  while 
with  bipolar  induction,  as  illustrated  in  the  cases  given  in 
Art.  3043  and  those  following,  the  E.  M.  F.  generated  in 
the  conductor  is  an  alternating  E.  M.  F. 

3061.  In  order  to  electrically  connect  a  stationary  ex- 
ternal circuit  with  the  moving  conductor,  some  form  of 
sliding  or  rubbing  contact  is  necessary,  which  usually  takes 
the  form  of  stationary  strips  of  copper,  carbon,  or  other  con- 
ducting material  called  brushes,  which  form  the  terminals 
of  the  external  circuit,  and  which  rest  upon  bare  metallic 
surfaces  which  are  electrically  connected  to  the  conductors 
and  mechanically  attached  to  but  insulated  from  the  shaft 
by  which  the  armature  core,  conductors,  and  collecting  de- 
vices are  driven.  In  case  it  is  desired  to  make  continuous 
connection  throughout  the  revolution  with  the  conductor, 
these  bare  metallic  surfaces  are  made  continuous,  i.  e.,  in 
the  form  of  rings,  and  the  device  is  then  called  a  collector, 
while  if  it  is  desired  to  make  the  connection  between  the 
conductors  and  the  external  circuit  during  a  part  of  a  revo- 
lution only,  the  bare  metallic  surfaces  are  made  segmental. 
It  is  never  the  case  that  the  external  circuit  is  entirely  dis- 


APPLIED   ELECTRICITY.  1931 

connected  from  all  the  conductors  of  the  armature  at  the 
same  time,  so  that  if  any  particular  conductor  is  discon- 
nected from  one  of  the  terminals  of  the  external  circuit  at 
any  time  during  the  revolution,  another  must  be  substi- 
tuted. This  results  in  a  collecting  apparatus  consisting  of 
a  series  of  separate  metallic  segments  arranged  in  cylindrical 
form,  each  connected  to  some  part  of  the  winding,  forming 
a  device  called  a  commutator. 

From  the  nature  of  the  device,  the  character  of  the  dif- 
ference of  potential  which  appears  between  the  terminals  of 
the  external  circuit  (the  brushes),  if  a  collector  is  used,  is 
the  same  as  the  character  of  the  E.  M.  F.  generated  in  the 
conductors;  i.  e. ,  it  is  subject  to  the  same  fluctuations  in 
value  or  reversals  of  direction. 

If  a  coniDmtator  is  used,  this  is  not  necessarily  the  case; 
in  fact,  is  not  likely  to  be,  since  the  connection  with  any 
particular  conductor  is  not  maintained  throughout  that 
conductor's  cycle  of  motion,  so  that  the  character  of  the 
E.  M.  F.  generated  is  not  reproduced  in  the  difference  of 
potential  existing  between  the  brushes.  This  is  an  impor- 
tant distinction,  since  it  is  the  character  of  this  difference  of 
potentiai  which  directly  determines  that  of  the  current  in 
the  external  circuit,  and  not  the  character  of  the  E.  M.  F. 
generated. 

3062.  It  has  been  pointed  out  that,  in  order  to  gener- 
ate a  sufficiently  high  E.  M.  F.  for  commercial  applications, 
a  number  of  conductors  must  be  used,  so  connected  together 
that  their  E.  M.  F. 's  will  add  together  to  the  desired 
amount.  These  conductors  may  obviously  be  located  in  the 
same  magnetic  field,  and  rotated  under  the  same  conditions; 
then,  the  E.  M.  F.  of  each  will  pass  through  exactly  the 
same  cycle,  with  a  phase  difference  depending  upon  their 
relative  positions  in  the  field  at  any  instant.  From  a  study 
of  these  features,  the  proper  methods  of  connecting  the  con- 
ductors to  each  other  and  to  the  external  circuit  to  attain 
any  desired  result  may  be  deduced. 

Fig.   1143    represents    16    conductors,  a,    b^   c^  .   .   .  .  J>, 


1932 


APPLIED   ELECTRICITY. 


equally  spaced  around  the  periphery  of  the  core   C.     The 
direction  of  the  lines  of  force  being  from  N  to  5,   and  the 

direction  of  motion 
being  as  indicated 
by  the  arrows,  the 
direction  of  the  E. 
M.  F.  in  the  con- 
ductors under  the  N 
pole  face  is  from 
back  to  front,  while 
in  those  under  the  5 
pole  face  it  is  from 
front  to  back,  as 
will  be  seen  if  the 
hand  rule  (Art. 
2442)  is  appHed. 
Fig.  1143.  This  is  indicated  by 

marking  the  conductor  with  a  +  or  a  solid  black  dot,  as 
shown.  Conductors  in  the  positions  a  and  z,  being  in  such 
a  position  that  no  lines  of  force  are  cut  by  them,  have  no 
E.  M.  P.,  and  are  not  marked. 

3063.  In  connecting  two  or  more  conductors  in  series, 
it  is  evident  that  the  maximum  E.  M.  F.  will  result  when 
the  E.  M.  F. 's  of  the  two  conductors  coincide  in  phase,  for, 
otherwise,  at  a  part  of  their  cycle  the  E.  M.  F.'s  in  the  two 
conductors  would  oppose  each  other;  the  same  result  may 
be  obtained  if  the  phases  are  displaced  180°,  for  then  the 
two  conductors  will  each  have  a  maximum  E.  M.  F.  gen- 
erated in  them  at  the  same  instant,  and  al- 
though these  two  E.  M.  F.'s  would  be  repre-  ^& 
sented  in  a  clock  diagram  as  acting  in  opposite 
directions,  the  conductors  may  be  so  connected 
that  the  E.  M.  F.'s  will  add  together.  This  is 
represented  by  the  diagram.  Fig.  1144,  where 
a  b  and  c  d  represent  two  conductors,  in  which 
the  E.  M.  F.'s  generated  are  in  opposite  direc-  ^ 
tions,   as  indicated  by  the  arrow-heads,  but  by        fig,  ii44. 


APPLIED   ELECTRICITY.  1933 

connecting  the  ends  b  and  c  together  the  difference  of 
potential  between  a  and  d  is  equal  to  the  sum  of  the  two 
E.  M.  F.'s. 

Applying  these  principles  to  the  case  illustrated  in  Fig. 
1144,  it  is  evident  that  the  proper  conductor  with  which  any 
one  of  the  conductors — for  example,  conductor  e — should 
be  connected  in  series  is  either  the  conductor  diametrically 
opposite  it,  in  this  case  conductor  ;;z,  or  either  of  the  con- 
ductors immediately  adjacent  to  it,  in  this  case  either  con- 
ductoryor  d. 

Note. — The  figure  being  very  much  out  of  proportion,  the  angular 
distance  between  these  adjacent  conductors  would  seem  to  be  sufficient 
to  cause  a  considerable  difference  in  their  phase ;  in  practice,  however, 
the  angular  distance  between  adjacent  conductors  would  be  very- 
small,  and  the  difference  in  phase  of  the  E.  M.  F.'s  generated  in  them 
almost  inappreciable. 

3064.  Applying  the  principle  illustrated  in  Fig.  1144, 
opposite  conductors  would  be  connected  by  conductors  ex- 
tending across  one  of  the  end  faces  of  the  core.  But  in 
connecting  adjacent  conductors  in  series  a 
different  method  must  be  followed,  since  the 
ends  which  are  similarly  situated  on  the  core 
must  be  connected  together,  as  illustrated  in 
Fig.  1145,  where  a  b  and  c  d  represent  two 
conductors,  in  each  of  which  the  E.  M.  F. 
generated  is  in  the  same  direction,  as  indicated 
by  the  arrow-heads.  In  order  to  connect  these 
two  conductors  in  series,  so  that  the  E.  M.  F.'s 
will  add,  the  ends  b  and  d  (or  a  and  c)  must  be  connected 
together,  as  represented,  in  which  case  the  difference  of 
potential  between  a  and  c  (or  b  and  d,  if  a  and  c  are  con- 
nected) would  be  equal  to  the  sum  of  the  two  E.  M.  F.'s 
generated. 

3065.  Now,  in  the  armature,  the  above  connection  mani- 
festly can  not  be  made  across  the  end  faces  of  the  drum; 
neither  can  it  be  made  directly  across  the  cylindrical  face,  for 
in  the  latter  case  an  E.  M.  F.  would  be  set  up  in  the  con- 
necting wire,   opposite  in  direction  to  the  E.  M.  F.  of  the 


1934 


APPLIED  ELECTRICITY. 


:S^:1i 

&-"" 

,-- — 

— ■«--i- 

■IZ^   "" 

■^.,,,^ 

-<-V- 

-i^     "- 

•-^  ^^^ 

-<--V 

Sr^--' 

;:;;: 

<- 

-Va- 

~-- 

::\^ 

,¥- 

1^ 

-* 

conductors.     The  only  reasonable  way  in  which  this  style 

of    connection    can 


be  made  is  to  make 
the  armature  core 
in  the  form  of  a  cy/- 
indrical  ring,  and 
pass  the  connecting 
'  wires  through  the 
hole  in  the  center  of 
the  ring,  as  illus- 
trated in  Fig.  1146. 
Here  the  conductor 
c  is  connected  to 
the  conductor  d  by 
Pi^-  ^^40.  a  wire  passing  down 

the  back  face  of  the  ring,  through  the  hole  in  the  center  at 

X  and  up  the  front  face  to  d. 

The  lines  of  force  pass  from  pole  to  pole    through    the 

iron  of  the  core,  as  represented  in  Fig.  1146,  and  hence  are 

not  cut  by  this  connecting  wire  x,  which,  therefore,  has  no 

E.  M,  F.  generated  in  it. 

3066.  These  two  general  methods  of  connecting  con- 
ductors in  series  are  called  drum  >vinding  and  ring 
winding,  respectively,  from  the  shape  of  the  cores  used. 
The  first  practical  use  of  the  ring  winding  was  due  to 
Gramme,  hence  it  is  often  called  the  Gramme  winding. 
It  was  invented  by  Paccinotti.  The  drum  winding  was 
originated  by  Siemens. 

3067.  In  building  up  a  drum  armature  core,  the  disks 
of  which  it  is  composed  may  be  slipped  directly  on  the 
driving  shaft,  forming  a  solid  mass  of  metal;  but  in  the 
ring  core  it  is  necessary  to  provide  a  support  for  the  ring- 
shaped  disks,  which  shall  have  sufficient  strength  to  drive 
the  armature  core  and  at  the  same  time  provide  a  sufficient 
opening  between  the  shaft  and  the  inside  of  the  core  to  admit 
the  connecting  wires  of  the  winding.  Such  a  support  is 
called  a  spider,  and  usually  consists  of  two  castings,  made 


APPLIED   ELECTRICITY.  1935 

with  a  central  hub  bored  out  for  the  shaft,  from  which  hub 
a  number  of  thin  arms  radiate  and  support  the  armature 
core,  the  connecting  Avires  being  wound  in  between  these 
arms. 

3068.  It  will  be  seen  that  if  the  conductors  are  ar- 
ranged radially  on  the  end  faces  of  the  core,  with  the  pole- 
pieces  facing  these  surfaces  (see  Art.  3055),  the  same  two 
systems  of  winding  may  be  followed  when  connecting  the 
conductors  in  series.  In  this  case  the  connecting  wires  are 
arranged  on  the  cylindrical  surface  (or  surfaces  in  a  ring 
winding)  instead  of  the  radial  surfaces.  To  get  the  best  re- 
sults, these  armatures  are  made  in  the  form  of  a  disk;  the 
distinctive  features  of  the  ring  or  drum  winding  are  not 
altered  by  this  change  in  the  form  of  the  core,  but  the  me- 
chanical construction  is  materially  different. 

In  order  to  distinguish  between  the  two  forms  of  cores, 
those  in  which  the  lines  of  force  enter  and  leave  the  cores 
at  the  cylindrical  surface  are  called  cylinder  armatures, 
whether  the  winding  be  ring  or  drum,  and  those  in  which 
the  lines  of  force  enter  and  leave  at  the  end  face  (or  faces) 
are  called  disk  armatures.      (vSee  Arts.  3041  and  3042.) 

3069.  Fig.  1147  illustrates  these  two  methods  of  con- 
necting conductors  in  series  for  cylinder  amatures,  (/i)  being 
the  ring  and  (i>)  the  drum  winding.  In  each  the  upper  half 
of  the  core  is  removed,  showing  the  loop  formed  by  the  con- 
ductors and  the  connections  between  them.  In  order  to 
connect  the  free  ends  of  "the  loop  to  the  collecting  device,  or 
to  other  conductors,  other  connecting  wires  are  added,  as 
represented  at  1,  2.  It  will  be  seen  that  in  either  form  of 
winding  the  active  conductors  and  the  connecting  wires 
form  a  coil  of  one  or  more  turns.  In  practice  these  coils  are 
usually  formed  from  a  single  piece  of  insulated  wire,  of  suit- 
able length,  wrapped  around  the  core  a  sufificient  number  of 
times  to  make  the  coil  of  the  requisite  number  of  turns. 
Each  coil  so  wound  covers  a  certain  fraction  of  the  surface 
of  the  armature  core;  in  the  case  of  the  drum  winding,  this 


1936 


APPLIED   ELECTRICITY. 


fraction  of  the  surface  is  divided  into  two  parts  that  are  on 
opposite  sides  of  the  core,  while  in  the  ring  winding  it  is 


Fig.  1147. 

altogether  on  one  side.     The  amount  of  surface  of  the  core 
covered  by  the  coil  may  be  called  the  width  of  the  coil. 


DIRECT-CURRENT   ARMATURE    WIND- 
INGS. 


UNIPOLAR  ARMATURES. 

3070.  In  order  that  an  E.  M.  F.  which  acts  continually 
in  one  direction  may  be  generated  in  a  moving  conductor, 
it  is  necessary  that  the  direction  of  motion  of  the  conductor 
be  always  the  same  with  reference  to  the  direction  of  the 
lines  of  force  of  the  magnetic  field  in  which  the  motion  takes 
place.  Motion  in  a  straight  line  is  here  obviously  impossi- 
ble, since  it  could  not  be  continued  for  any  length  of  time ; 
motion  in  a  circular  path  is,  therefore,  the  only  kind  that 
ansvvers  the  requirements. 

In  Arts.  3041  and  3042  two  methods  of  moving  a  con- 
ductor in  a  circular  path  in  a  constant  direction  relative  to 
the  lines  of  force  are  described  and  illustrated.  These  are 
examples  of  wiipolar  induction.  (See  Art.  3059.)  In 
either  of  the  above  methods,  it  is  evident  that  a  number  of 


APPLIED   ELECTRICITY.  1937 

conductors  may  be  used,  distributed  along  their  circular 
path,  and  in  each  the  same  E.  M.  F,  will  be  generated.  In 
order  to  obtain  a  high  E.  M.  F.,  it  would  then  be  desirable 
to  connect  these  various  conductors  in  series,  in  such  a  way 
that  all  their  E.  M.  F.'s  would  be  added  together. 

If  this  is  attempted,  it  will  be  found  that,  owing  to  the 
fact  that  the  lines  of  force  form  closed  loops,  it  is  impossi- 
ble to  permanently  connect  the  active  conductors  in  series  in 
any  manner  so  that  the  connecting  wires  will  not  cut  the 
lines  of  force  in  such  a  way  as  to  set  up  in  them  an  opposing 
E.  M.  F.  of  exactly  the  same  value  as  that  generated  in  the 
armature  conductors  proper.  The  final  effect  of  connecting 
any  number  of  armature  conductors  in  series  is,  therefore, 
at  most  only  the  E.  M.  F.  of  a  single  conductor. 

The  only  way,  then,  in  which  the  conductors  may  be  con- 
nected is  by  means  of  sliding  contacts,  whereby  the  con- 
necting wires  may  be  stationary  with  respect  to  the  moving 
armature  conductors. 

It  is  evident  that  this  method  is  of  limited  application, 
since  the  connections  for  a  large  number  of  conductors 
would  become  too  complicated. 

3071.  With  unipolar  induction,  then,  the  maximum 
E.  M.  F.  possible  is  that  of  a  single  conductor;  it  is  evident, 
however,  that  if  a  number  of  separate  conductors  are  used, 
they  may  all  be  connected  in  parallel,  which,  while  it  does 
not  increase  the  E.  M.  F.,  does  increase  the  possible  current 
output,  since  it  decreases  the  internal  resistance  of  the  arma- 
ture winding. 

A  number  of  such  conductors  connected  in  parallel  are 
equivalent  to  a  single  wide  conductor;  in  the  case  illustrated 
in  Fig.  1131,  this  would  be  equivalent  to  a  tube,  of  a  thick- 
ness sufficient  to  allow  it  to  rotate  freely  between  the  poles 
A^and  5,  while  in  the  case  illustrated  in  Fig.  1132  it  would 
be  equivalent  to  a  disk  rotating  between  the  poles  N  and  S. 

It  is  in  one  or  the  other  of  these  forms  that  the  armatures 
of  unipolar  dynamos,  which  have  a  limited  application  in 
cases  where  a  large  current  at  a  low  potential  is  required,  are 
constructed. 


1938 


APPLIED   ELECTRICITY. 


OPEN-COIL    BIPOLAR    ARMATURES. 

3072.  The  E.  M.  F.  generated  in  the  separate  coils  of 
an  armature  winding  which  is  revolved  between  the  oppo- 
site poles  of  a  bipolar  magnet  is  naturally  alternating  in 
character,  since  its  direction  when  passing  through  one  field 
is  opposite  to  that  which  it  has  when  passing  through  the 
other. 

When  connected  to  the  external  circuit  by  means  of  col- 
lector rings,  this  alternating  E.  M.  F.  is  impressed  directly 
on  the  external  circuit;  but  by  using  a  suitably  arranged 
commutator,  the  connections  between  the  coils  of  the  arma- 
ture winding  and  the  external  circuit  may  be  reversed  at 
proper  intervals,  so  that  the  current  in  the  external  circuit 
will  be  uniform  in  direction. 

A  simple  way  of  accomplishing  this  result  with  a  single 
coil  is  shown  in  Fig.    1148,   in  which   a  coil  of  three  con- 


ductors, a  b  c,  is  wound  on  a  ring  core  and  connected  to  the 
two  commutator  segments  S'  and  S",  each  of  which  covers 
nearly  one-half  the  circumference   of  the  commutator.     On 


APPLIED   ELECTRICITY.  1939 

these  two  segments  rest  the  two  brushes  -}-B  and  —B,  they 
being  placed  opposite  each  other  and  making  contact  with 
the  segments  S'  and  S"  on  the  neutral  line  x  _y. 

3073.  When  the  coil  is  in  the  position  shown,  it  being 
rotated  in  the  direction  indicated  by  the  arrow,  the  E.  M.  F. 
generated  in  the  coil  will  be  acting  in  the  direction  indicated 
by  the  arrow-heads,  thus  making  the  top  brush  positive. 
When  the  coil  reaches  the  neutral  space,  the  brushes  will  each 
momentarily  make  contact  with  both  commutator  segments, 
by  bridging  the  space  which  separates  them ;  but  as  in  this 
position  there  is  no  E.  M.  F.  generated  in  the  coil,  this  has 
no  effect.  On  further  motion  of  the  coil  under  the  opposite 
pole-piece,  by  which  its  E.  M.  F.  is  reversed  in  direction, 
the  top  brush  comes  in  contact  with  segment  S'  and  the 
bottom  brush  with  segment  S".  Since  the  direction  of  the 
E.  M.  F.  in  the  coil  has  been  reversed,  this  reversal  of  the 
connection  between  the  brushes  and  segments  results  in 
keeping  the  difference  of  potential  between  the  brushes  in 
the  same  direction  as  before. 

It  is  evident  that  this  difference  of  potential  is  not  at  all 
constant,  but  varies  from  a  maximum  to  zero  and  then  to 
maximum  again;  the  curve  of  its  various  instantaneous 
values  would  be  a  series  of  waves,  all  on  one  side  of  the  base 
line.  In  other  words,  such  an  arrangement  as  has  been 
described  would  cause  a  pulsating  current  to  flow  in  the  ex- 
ternal circuit.     (See  Art.  3056.) 

3074.  Another  coil  can  be  wound  on  the  core  directly 
opposite  the  first,  and  connected  in  series  or  in  parallel  with 
it.  The  width  of  the  coils  can  not  be  greater  than  the  width 
of  the  neutral  spaces,  without  causing  opposing  E.  M.  F.'s 
during  parts  of  a  revolution;  consequently,  only  a  part  of 
the  surface  of  the  armature  can  be  utilized,  and  at  best  there 
is  a  part  of  the  time  that  the  E.  M.  F.  of  the  winding  is 
zero. 

However,  other  pairs  of  coils  may  be  wound  on  the  sur- 
face of  the  core,  in  positions  intermediate  between  those  of 


1940 


APPLIED   ELECTRICITY. 


the  original  pair;  these  pairs  may  then  each  have  its  own 
commutator  and  brushes,  and  as  the  maximum  and  zero  of 
values  of  the  E.  M.  F.'s  of  the  new  windings  occur  at  differ- 
ent periods  of  time  from  those  of  the  first  pair,  the  E.  M.  F.'s 
may  be  combined  so  as  to  prevent  the  E.  M.  F.  acting  in 
the  external  circuit  from  falling  to  zero. 

3075.     Fig.  1149  shows  the  arrangement,  for  both  ring 
and  drum  winding,  of  two  sets  of  coils  A  A'  and  B  B\  each 


Fig.  1149. 

set  containing  four  active  conductors,  those  of  one  set 
occupying  a  position  on  the  core  90°  from  those  of  the  other. 
Both  sets  are  supplied  with  their  two-segment  commutators, 
which  for  convenience  are  represented  as  being  concentric, 
A  A'  being  connected  to  a  and  a\  and  B  B'  to  b  and  b'. 
Brushes  1  and  2  rest  on  segments  a  and  a',  and  brushes 
3  and  4  rest  on  segments  b  and  b'. 

3076.  The  maximum  E.  M.  F.  of  each  of  these  sets  is 
the  same,  but  that  of  the  one  occurs  \  revolution  ahead  of 
the  other,  so  that  the  curves  representing  the  instantaneous 
values  of  the  E.  M.  F.'s  of  these  two  sets  of  coils  for  one 
revolution  would  be  about  as  represented  in  Fig.  1150,  where 
curve  1  is  the  E.  M.  F  of  coils  A  and  A',  and  curve  2  is  the 
E.  M.  F.  of  coils  B  and  B',  for  a  complete  revolution,  start- 
ing from  the  position  of  the  coils  represented  in  Fig.  1149. 

If  the  two  sets  of  coils  are  connected  together  in  series  by 


APPLIED   ELECTRICITY. 


1941 


means  of  an  external  connection  between,  say,  brushes  2  and 
S,  then  the  difference  of  potential  between  brushes  1  and  ^ 
at  any  instant  is  equal  to  the  sum  of  the  E.  M.  F.'s  of  the 


--, 

~-- 

~^ 

is 

\ 

/ 

f3 

\ 

Is 

\ 

1 

\ 

1 

/ 

1 

\ 

1 

\ 

+ 

J 

\ 

/ 

\ 

\ 

1 

/ 

\ 

\ 
\ 

1 

71 

f\ 

> 

7i 

\ 

' 

> 

C 

ii 

\ 

/- 

% 

/. 

\ 

7 

1 

\ 

/ 

\ 

1 

/ 

\ 

J 

V 

J 

V 

J 

V 

J 

\ 

i 

r 

y 

f}" 

li 

iO" 

270" 

360 

Fig.  1150. 

two  sets  of  coils  at  that  instant.  The  result  of  the  addition 
for  the  entire  revolution  is  represented  by  the  dotted  curve 
3,  Fig.  1150. 

It  is  readily  seen  that  for  about  one-fourth  of  each  wave 
the  E.  M.  F.  of  one  set  of  coils  is  nearly  at  its  zero  value, 
and,  therefore,  contributes  but  little  to  the  total  E.  M.  F. 
of  the  armature;  the  resistance  of  this  set  of  coils  must, 
nevertheless,  be  overcome,  since  it  forms  a  part  of  the 
circuit. 

3077.  Instead  of  connecting  the  sets  of  coils  in  series, 
they  may  be  connected  in  parallel;  but  with  the  coils  con- 
nected as  shown  in  Fig.  1149,  this  would  result  in  having 
the  more  active  set  of  coils  short-circuited  by  the  set  that  is 
less  active,  which  would  very  materially  reduce  the  differ- 
ence of  potential  between  the  brushes.  There  is,  however, 
a  part  of  the  revolution  when  the  E.  M.  F.'s  of  the  two  sets 
of  coils  are  nearly  enough  the  same  to  allow  of  their  being 
connected  together  in  parallel,  and  by  widening  the  gap  be- 
tween the  ends  of  the  segments  of  the  commutator,  each  set 
of  coils  may  be  entirely  disconnected  from  its  brushes  during 
the  part  of  its  revolution  when  its  E.  M.  F.  is  much  lower 
than  that  of  the  other  set. 


1943 


APPLIED   ELECTRICITY. 


This  arrangement  of  the  commutator  segments  for  the 
windings  shown  in  Fig.  1149  is  represented  in  Fig.  1151,  in 

which  a  and  a'  are  the  segments 
connected  to  coils  A  and  A\  and 
b  and  b'  are  the  segments  con- 
nected to  coils  B  and  B\  as  be- 
fore. 


Fig.  1151. 
represents  the  E.  M.  F 


3078.  It  is  evident  that 
curves  showing  the  difference  of 
potential  between  either  pair  of 
brushes  would  comprise  that  part 
of  curves  i  or  ^  (Fig.  1150)  that 
of  the  winding  during  the  time  that 
the  brushes  are  in  contact  with  the  commutator  segments. 
The  curves  in  Fig.  1152  represent  the  difference  of  potential 
which  would  exist  between  the  brushes  if  the  arrangement 
shown  in  Fig.  1151  were  used  with  the  windings  shown  in  Fig. 
1149,  curves  i,  i,  etc.,  showing  the  difference  of  potential 
between  brushes  S  and  .^,  and  curves  2,  2,  etc.,  showing  the 
difference  of  potential  between  brushes  1  and  2,  starting  from 
the  position  of  the  commutator  represented  in  Fig.  1151.  It 
is  apparent  that  with  this  arrangement  the  windings  might  be 
connected  in  parallel  by  connecting  together  brushes  1  and 
S  and  2  and  4  (Fig.  1151).     In  that  case,  the  difference  of 


90^ 


180° 

Fig.  1152. 


270° 


360" 


potential  between  the  brushes  would  be  the  E.  M.  F.  of  one 
winding  until  the  other  is  connected  in  parallel  with  it, 
which  connection  would  cause  the  difference  of  potential  to 
drop  a  little,  since  the  winding  which  is  newly  connected 
has  a  slightly  lower  E.  M.  F.  than  the  other. 


The  result  of 


APPLIED   ELECTRICITY.  1943 

this  is  that  the  curve  is  depressed  a  little  during  the  time 
that  the  coils  are  in  parallel,  as  represented  by  the  dotted 
lines  in  Fig.  1152. 

3079.  From  this  curve  (Fig.  1152)  it  will  be  seen  that 
at  the  moment  when  the  two  sets  of  coils  are  thrown  in 
parallel  by  the  brushes,  the  E.  M.  F.  in  the  two  sets  is  not 
the  same,  that  of  the  set  which  had  just  before  alone  been 
connected  to  the  brushes  being  higher  than  that  of  the 
other.  A  little  later,  at  the  moment  when  one  of  the  sets 
is  disconnected  from  the  circuit  by  one  set  of  brushes  leav- 
ing its  segments,  the  coil  which  is  disconnected  has  a  less 
E.  M.  F.  than  the  other. 

If  the  coils  had  little  inductance,  this  would  result  in  the 
greater  E.  M.  F.  of  the  one  set  of  coils  sending  a  current 
around  through  the  other  set  against  the  E.  M.  F.  gener- 
ated in  it,  which  current  would  not  appear  in  the  external 
circuit,  and  would,  therefore,  represent  so  much  wasted 
energy. 

3080.  This  local  current  would  evidently  be  greatest 
when  the  difference  between  the  E.  M.  F.'s  of  the  two  sets 
of  coils  is  greatest;  that  is,  at  the  moment  when  the  two 
sets  of  coils  are  connected  in  parallel,  and  at  the  moment 
one  of  the  sets  is  disconnected  from  the  brushes. 

Then,  when  the  one  set  of  coils  is  disconnected  from  the 
other,  this  local  current  would  be  suddenly  broken,  which 
would  result  in  sparking. 

In  an  armature  as  actually  constructed,  however,  the 
inductance  of  the  coils  is  sufficient  to  prevent  these  local 
currents;  when  a  coil  is  first  connected  in  parallel  with 
another,  its  inductance  prevents  a  sudden  rush  of  current 
through  it,  and  allows  it  to  take  up  its  share  of  the  current 
output  gradually.  As  the  coil  approaches  the  point  where 
it  is  to  be  disconnected  from  the  circuit,  and  the  E.  M.  F. 
generated  in  it  becomes  less  than  that  of  the  coil  with  which 
it  is  connected,  its  inductance  serves  to  keep  up  its  E.  M.  F., 
so  that  its  current  gradually  grows  less,  until  at  the  time 
when   it  is  disconnected  from  the  circuit,  if  that  time  is 


1944 


APPLIED   ELECTRICITY. 


properly  chosen,  its  current  output  is  practically  zero,  and 
little  or  no  spark  results  from  breaking  its  connection  with 
the  circuit. 

3081.  In  Fig.  1151  the  two  sets  of  segments  have,  for 
convenience,  been  represented  as  concentric;  in  practice, 
however,  the  two  sets  would  be  made  of  the  same  diameter 
and  placed  side  by  side.  If  made  in  this  way,  the  separate 
brushes  1  and  S  and  2  and  ^  Fig.  1151,  may  be  replaced  by 
two  wider  brushes,  wide  enough  to  bear  on  either  or  both 
sets  of  segments.     This  is  represented  in  Fig.  1153,  in  which 

a  and  a'  and  b  and  b'  are  the  two 
pairs  of  commutator  segments, 
and  1  and  2  are  the  brushes, 
which  are  wide  enough  to  bear 
on  either  or  both  pairs  of  seg- 
ments, according  to  the  position 
of  the  commutator. 


3082.  It  will  be  seen  that 
this  arrangement  of  coils  and 
commutator  gives  a  direct  but 
pulsating  current,  in  which  the 
pulsations  are  not  excessive.  As 
pjq  ;[j5g_  has  been  pointed  out,  however, 

the  width  of  the  coils  should  not  be  greater  than  the  width 
of  the  neutral  spaces,  so  that  even  with  two  sets  of  coils  the 
entire  armature  surface  can  hardly  be  utilized. 

More  than  one  complete  winding,  however,  can  be  placed 
upon  the  same  core,  and  if  each  is  provided  with  its  own 
commutator,  they  may  be  coupled  up  in  series  or  in  parallel, 
as  desired. 

Such  a  winding  as  has  been  described,  in  which  separate 
sets  of  coils  are  used,  and  which  are  connected  together  in 
various  combinations  and  connected  to  or  disconnected  from 
the  circuit  during  the  rotation  of  the  armature,  is  called  an 
open-coil  >vinding. 

3083.  Only  two  or  three  forms  of  open-coil  windings 
are  m  commercial  use  at  the  present  time.     That  which  has 


APPLIED   ELECTRICITY. 


1945 


been  described  is  used  in  the  Brush,  dynamos,  the  ordinary 
sizes  of  machine  using  two  separate  windings,  each  with  its 
commutator,  as  represented  in  Fig.  1154. 

In  this  machine  the  pole-pieces  face  the  sides  of  the 
armature,  as  represented  by  the  heavy  dotted  lines.  The 
segments  of  the  two  separate  commutators  are  for  con- 
venience represented  as  concentric,  with  the  brushes  resting 
on   their  edges  ;    whereas,   actually,   they  lie   side  by  side, 


Fig.  1154. 

forming  two  separate  commutators  of  the  same  diameter, 
each  having  four  segments,  and  the  brushes  rest  on  their 
circumference. 

One  winding  consists  of  two  pairs  of  coils  A  and  A'  con- 
nected in  series,  and  B  and  B'  also  connected  in  series,  the 
two  pairs  being  located  at  right  angles  to  each  other,  as 
represented. 

This  winding  is  connected  to  its  commutator,  coil  A  to 
segment  a,  coil  A'  to  segment  a' ,  coil  B  to  segment  b,  and 
coil  B'  to  segment  b',  as  represented.     Brushes  1  and  2  rest 


1946  APPLIED   ELECTRICITY. 

on   this    commutator,    making  contact   on   the  line  x  j/  of 
maximum  action  of  the  coils. 

The  second  winding  consists  of  two  pairs  of  coils  C  and  C 
and  D  and  D',  located  at  right  angles  to  each  other  and  half 
way  between  the  coils  of  the  first  winding.  These  coils  are 
connected  in  series  and  to  the  segments  of  the  second  com- 
mutator, coil  C  to  segment  c,  coil  C  to  segment  c',  coil  D  to 
segment  d,  and  coil  D'  to  segment  d',  as  represented. 
Brushes  S  and  4  rest  upon  the  segments  of  this  commutator 
on  the  same  line  of  maximum  action  of  the  coils. 

3084.  Taking  each  winding  separately,  it  will  be  seen 
that  its  two  sets  of  coils  pass  through  the  following  combi- 
nations :  One  set  of  coils  only  connected  to  the  brushes  ; 
then  the  two  sets,  connected  in  parallel,  both  connected  to 
the  brushes;  then  one  set  only;  then  both  sets  in  parallel, 
and  so  on. 

The  maximum  E.  M.  F.  occurs  when  the  single  set  of 
coils  is  connected,  and  is  directly  in  the  line  of  maximum 
action  ;  the  minimum  occurs  -|  of  a  revolution  ahead  of  this 
point,  when  both  sets  of  coils  are  in  parallel,  and  are  equally 
distant  from  the  line  of  maximum  action.      (See  Fig.  1152.) 

This  being  the  case,  it  is  evident  that  as  the  coils  of  one 
winding  are  half  way  between  the  coils  of  the  other,  the 
maximum  E.  M.  F.  of  one  winding  occurs  at  the  same 
instant  as  does  the  minimum  E.  M.  F.  of  the  other.  On 
account  of  this,  when  the  two  windings  are  connected  in 
series,  the  fluctuations  of  the  current  are  much  reduced. 

This  connection  of  the  two  windings  is  obtained  by  con- 
necting the  positive  brush  {3,  Fig.  1154)  of  one  winding 
with  the  negative  {3,  Fig.  1154)  of  the  other,  the  external 
circuit  being  connected  between  the  two  remaining  brushes 
(1  and  4,  Fig.  1154). 

In  the  larger  sizes  of  these  machines,  three  and  even  four 
separate  windings  are  used,  each  with  its  commutator 
and  all  connected  in  series. 

3085.  Instead  of  using  overlapping  segments,  the  same 
results   may  be  obtained  with  segments  which  are  placed 


APPLIED   ELECTRICITY.  1947 

end  to  end,  by  making  the  brushes  have  a  large  arc  of 
contact,  or,  what  amounts  to  the  same  thing,  using  two 
brushes  on  each  side,  spaced  a  distance  equal  to  the  desired 
arc  of  contact  and  connected  permanently  together.  This 
is  represented  in  Fig.  1155,  a  and  a'  being  the  segments 
connected  to  winding  A  A' 
(Fig.  1149),  and  b  and  b'  being 
the  segments  connected  to  wind- 
ing B  B'  (Fig.  1149).  It  will 
be  seen  that  the  pairs  of  brushes 
1  and  3  and  Jf  and  2,  being  per- 
manently connected  together, 
act  as  one  wide  brush.  In  the 
position  shown,  both  sets  of 
coils  are  in  parallel ;  if  the  com- 
mutator is  rotated  in  the  di-  fig.  1155. 
rection  of  the  arrow,  segments  a  and  a'  will  pass  out  from 
under  brushes  3  and  Jf,  leaving  only  segments  b  and  b'  con- 
nected to  the  winding,  and,  therefore,  only  coils  B  and  B'  in 
circuit.  Further  rotation  will  bring  segments  a  and  a' 
under  brushes  1  and  ^,  respectively,  throwing  coils  yi  and  A' 
and  B  and  B'  in  parallel  again,  and  so  on.  It  will  be  seen 
that  this  arrangement  gives  the  same  results  as  that  pre- 
viously considered. 

3086.  Instead  of  two  sets  of  coils,  three  may  be  used, 
situated  120°  apart  on  the  armature. 

In  this  arrangement,  which  is  used  in  the  Thomson- 
Houston  open-coil  dynamos,  only  one  end  of  each  set  of 
coils  is  carried  to  a  commutator  segment,  there  being,  there- 
fore, but  three  segments;  the  other  end  is  connected  to  a 
common  junction  of  the  three  ends. 

The  commutator  segments  are  each  a  little  less  than 
130°  in  span,  being  placed  end  to  end  and  separated  by  a 
small  air-gap. 

The  brushes  used  are  divided  into  pairs,  as  described  in 
Art.  3085  ;  that  is,  the  equivalent  of  two  wide  brushes  is 
used,  the  arc  of  contact  being  about  60°,  or  about  half  the 
span  of  one  segment. 


1948 


APPLIED   ELECTRICITY. 


Both  ring  and  drum  windings  are  used  for  the  armatures; 
Fig.  1156  gives  a  diagram  of  the  connections,  etc.,  of  the 
drum-wound  armature.  A  A',  B  B\  and  C  C  are  the  three 
coils,  wound  on  the  core  in  planes  making  angles  of 
120°  with  each  other.  One  end  of  each  of  the  coils  is  joined 
to  a  metal  ring  (not  represented  in  the  figure)  on  the  back  of 


Fig.  1156. 
the  armature,  which  forms  a  common  connection  for  the 
three.  The  other  ends  are  joined  to  the  commutator  seg- 
ments, that  of  A  A'  to  segment  a,  that  of  B  B'  to  segment 
b^  and  that  of  C  C  to  segment  ^,  as  represented,  i,  ^,  <?, 
and  4  are  the  brushes,  as  before.  Those  numbered  ^  and  Jf. 
are  usually  called  the  priniary  brushes,  and  1  and  3  the  sec- 
ondary  brushes,  to  distinguish  them. 

3087.  From  the  diagram  (Fig.  1156)  it  will  be  seen 
that  coW  A  A',  though  half  way  between  the  pole-pieces,  is 
partly  active,  since  the  neutral  line  is  shifted  forwards  in  a 
manner  which  will  be  taken  up  later,  into  the  position  indi- 
cated by  the  line  x y.  This  coil  A  A'  is  connected  in  paral- 
lel with  the  coil  B  B'  by  the  two  positive  brushes,  and  the 
two  are  in  series  with  coil  C  C.  If  the  armature  be  consid- 
ered as  moving  in  the  direction  indicated  by  the  arrow,  it 
will  be  seen  that  as  coil  A  A'  gets  to  the  position  of  least 


APPLIED   ELECTRICITY.  1949 

action,  it  is  disconnected  from  the  circuit  by  segment  a  pass- 
ing out  from  under  brush  5,  leaving  coil  B  B'  and  coil  C  C 
in  series.  However,  as  the  distance  between  brush  8  and 
brush  2  is  only  slightly  greater  than  the  span  of  one  seg- 
ment, coil  A  A'  is  almost  immediately  connected  in  parallel 
with  coil  C  C,  as  segment  a  passes  under  brush  2,  making 
the  following  combination:  coil  B  B'  in  series  with  coils 
A  A'  and  C  C  in  parallel. 

As  the  rotation  of  the  armature  continues,  coil  C  C  is 
disconnected  from  the  negative  brush  1  and  connected  to 
the  positive  brush  ^,  being  thus  thrown  in  parallel  with  coil 
B  B' ,  the  two  being  then  in  series  with  coil  A  A'. 

Completing  the  half  revolution,  coil  B  B'  is  disconnected 
from  the  positive  brush  3  and  is  joined  in  parallel  with  coil 
A  A'  hy  the  two  negative  brushes  1  and  S,  leaving  coil  C  C 
connected  to  the  positive  brushes. 

Further  rotation  of  the  armature  repeats  this  series  of 
connections;  that  is,  during  every  half  revolution,  one  of 
the  coils  {^A  A'  in  the  preceding  paragraphs)  is  first  in  paral- 
lel with  the  coil  behind  it,  then  momentarily  disconnected 
from  the  circuit,  then  connected  in  parallel  with  the  coil 
ahead  of  it,  then  connected  in  series  with  the  other  two, 
which  are  then  in  parallel. 

3088.  From  the  diagram  (Fig.  1156)  it  will  be  seen 
that  when  a  coil  is  disconnected  from  one  set  of  brushes  it 
is  very  nearly  in  the  position  of  least  action,  and  the  coil 
with  which  it  was  just  before  connected  in  parallel  has  the 
higher  E.  M.  F.  of  the  two.  As  explained  in  Art.  3080, 
the  self-induction  of  the  coil  prevents  the  higher  E.  M.  F. 
of  the  olfher  sending  a  current  through  it  in  opposition  to 
its  own  E.  M.  F.  at  the  time  when  they  are  connected  in 
parallel;  in  fact,  when  a  coil  is  disconnected  from  its  mate 
it  is  still  supplying  some  of  the  current,  so  that  there  is  a 
spark  at  the  brushes. 

There  being  but  three  sets  of  coils  in  this  machine,  a 
great  number  of  turns  must  be  used  in  each  coil  to  give  the 
required  E.  M.  F.,  which  gives  each  set  of  coils  a  high  in- 
ductance.    This  lessens  to  a  great  extent  the  fluctuations 


1950  APPLIED  ELECTRICITY. 

in  the  E.  M.  F.  acting  on  the  external  circuit,  which  would 
otherwise,  owing  to  the  small  number  of  coils  used  and  the 
changes  in  the  manner  in  which  they  are  interconnected, 
be  very  considerable. 

3089.  Since  only  a  very  small  fraction  of  a  revolution 
carries  a  segment  from  contact  with  one  set  of  brushes  to 
contact  with  the  other,  a  slight  increase  in  the  arc  of  con- 
tact of  the  sets  of  brushes  would  allow  each  segment  of  the 
commutator  to  momentarily  be  in  contact  with  both  sets  of 
brushes  at  the  same  time;  the  effect  of  this  is  evidently  to 
short-circuit  the  armature,  thus  reducing  the  difference 
of  potential  between  the  brushes  (momentarily)  to  zero. 

There  being  two  places  where  the  short  circuit  occurs, 
i.  e.,  between  brushes  1  and  If.  and  2  and  5,  and  there  being 
three  commutator  segments,  six  short  circuits  occur  during 
every  revolution,  and  if  the  armature  is  revolving  at  850 
revolutions  per  minute,  there  are  6  X  850  =  5,100  short 
circuits  every  minute;  each  can,  therefore,  last  only  an  ex- 
tremely short  time,  and  the  high  inductance  of  the  arma- 
ture coils  prevents  any  excessive  flow  of  current  from  one 
to  the  other  through  the  short  circuit.  It  will  be  seen 
that  this  short-circuiting  of  the  armature  does  not  reduce 
the  maximum  value  of  the  E.  M.  F.,  but  as  it  introduces 
periods  in  each  revolution  where  the  difference  of  potential 
between  the  brushes  is  zero,  it  does  reduce  the  effective 
E.  M.  F.  acting  on  the  circuit.  By  varying  the  arc  of  con- 
tact of  the  brushes,  and  thus  varying  the  length  of  time  in 
each  revolution  that  the  armature  is  short-circuited,  the 
effective  E.  M.  F.  of  the  machine  may  be  varied  within 
comparatively  wide  limits. 


OPEN-COIL  MULTIPOLAR  ARMATURES. 
3090.  Thus  far  the  open-coil  winding  has  only  been 
considered  with  reference  to  bipolar  fields.  It  is  evident, 
however,  that  introducing  multipolar  fields  will  only  result 
in  a  duplication  of  the  parts  used  with  a  bipolar  field  for 
each  pair  of  poles  of  the  multipolar  field.     Thus,  for  a  wind- 


APPLIED   ELECTRICITY.  1951 

ing  for  a  four-pole  field   equivalent  to  that  shown  in  Fig. 
1149,  four  coils  would  be  required  in  each  set. 

Since  each  set  would  have  to  go  through  its  various  com- 
binations of  connections  during  each  half  revolution,  instead 
of  each  revolution,  it  is  evident  that  twice  as  many  com- 
mutator segments,  of  one-half  the  span,  would  be  required, 
or,  rather,  each  segment  would  be  divided  into  two.  These 
two  parts  of  the  segment  would  be  situated  directly  opposite 
each  other,  and  either  four  brushes  would  be  used  on  each 
commutator,  of  which  the  opposite  brushes  would  have  to  be 
connected  together,  or  the  opposite  commutator  segments 
would  be  permanently  connected  together,  and  only  two 
brushes  would  be  used.  This  latter  plan  is  best,  as  perma- 
nent connections  are  less  difficult  to  maintain  than  sliding 
connections. 

3091.  A  form  of  multipolar  open-coil  armature  which 
differs  slightly  from  the  above  description  is  used  in  the 
Westinghouse  open-coil  dynamo.  A  diagram  of  the  con- 
nections of  this  armature  is  given  in  Fig.  1157. 

The  two  commutators  are  represented  as  concentric, 
though  they  are  actually  side  by  side  on  the  shaft,  and,  as 
in  the  Brush  machine.  Fig.  1154,  are  situated  on  the  end  of 
the  shaft  outside  one  of  the  bearings,  the  leads  to  the  com- 
mutator being  brought  out  through  a  hole  in  the  shaft,  in- 
stead of  being  connected  directly,  as  represented  in  the  dia- ' 
gram. 

This  type  of  machine  employs  a  field-magnet  with  six 
poles ;  the  armature  is  drum-wound,  but  instead  of  the  coils 
being  laid  flat  on  the  surface  of  the  core,  they  are  wound 
around  eight  projecting  teeth  on  the  armature  core,  there 
being,  therefore,  eight  armature  coils.  This  armature 
winding,  as  in  the  Brush  machine,  is  divided  into  two  sepa- 
rate windings,  each  consisting  of  two  pairs  of  opposite  coils, 
and  each  connected  to  a  separate  commutator.  The  com- 
bination of  connections  of  the  various  sets  of  coils  is  similar 
to  that  of  the  Brush  machine;  that  is,  the  set  of  coils  in  the 
position    of  least  action   is  disconnected  entirely  from  the 


1952 


APPLIED  ELECTRICITY. 


circuit;  those  near  the  position  of  maximum  action  are  con- 
nected in  parallel,  and  in  series  (by  external  connection  of 
the  brushes)  with  that  set  which  is  actually  in  the  position 
of  maximum  action. 

In  this  style  of  winding,  any  coil,  such  as  A,  is  in  the  posi- 
tion of  least  action  when  the  projection  on  which  it  is  wound 


Fig.  1157. 

is  directly  under  a  pole-piece,  as  at  N;  for  when  in  this  posi- 
tion all  the  lines  of  force  from  the  pole-piece  N  pass  directly 
through  the  center  of  the  coil,  which,  therefore,  cuts  none  of 
the  lines  of  force.  As  soon  as  the  coil  moves  from  this  posi- 
tion, one  side  begins  to  cut  the  lines  of  force  of  the  pole- 
piece  A^as  it  passes  from  in  front  of  it,  and  as  it  moves  still 
farther,  the  ot/ier  side  of  the  coil  begins  to  cut  the  lines  of 
force  of  the  pole-piece  S,  towards  which  it  is  moving,  so 
that  when  half  way  between  the  two  poles  N  and  5,  both 
sides  of  the  coil  are  cutting  lines  of  force  equally  and  at  the 
maximum  rate,  and  this  is,  therefore,  the  position  of  maxi- 
mum action.     With  eight  coils  and  six  pole-pieces,  only  two 


APPLIED  ELECTRICITY.  1953 

(opposite)  coils  can  each  be  directly  under  a  pole-piece  at  the 
same  instant. 

3093.  Referring  to  Fig.  1157,  the  two  pairs  of  coils 
A  and  A'  and  B  and  B'  make  up  one  winding,  and  are  con- 
nected to  one  commutator,  as  shown.  The  two  opposite 
coils  A  and  A',  and  also  B  and  B' ,  are  connected  in  series 
by  connections  across  the  back  of  the  armature  core  (not 
shown  in  the  diagram). 

The  other  winding  is  made  up  of  the  two  pairs  of  coils 
C  and  C  and  D  and  D' ,  the  coils  of  each  pair  being  con- 
nected in  series,  and  to  the  other  commutator,  as  before. 

It  will  be  seen  that  each  commutator  is  made  up  of  twelve 
segments  separated  by  a  considerable  width  of  insulating 
material  (indicated  by  the  solid  black  parts).  These  twelve 
segments  are  connected  together  by  cross-connecting  wires 
in  four  sets  (one  for  each  coil  of  the  windings),  of  three 
segments  each  (one  for  each  pair  of  poles). 

Two  sets  of  brushes  are  used  on  each  commutator,  each 
set  consisting  of  two  brushes,  permanently  connected 
together,  which  rest  on  the  commutator  a  distance  apart 
equal  to  the  span  of  one  segment,  as  shown  at  1,  1'  or  2,  2'. 

It  will  be  seen  that  the  positions  of  the  commutator  seg- 
ments and  brushes  are  so  arranged  that  when  the  brushes 
of  one  commutator  bear  on  the  ends  of  single  segments,  the 
brushes  of  the  other  commutator  bear  on  the  middle  points 
of  the  adjacent  segments,  and  vice  versa. 

3093.  When  the  armature  is  in  the  position  repre- 
sented in  Fig.  1157,  coils  A  and  A'  are  in  the  position  of 
least  action,  and  are  disconnected  from  the  external  circuit. 
The  other  set  of  coils  B  and  B'  of  this  winding  is,  however, 
in  the  position  of  maximum  action,  and  is  connected  to  the 
circuit  through  brushes  1  and  1'  and  2  and  2',  which  rest 
on  segments  b  and  //,  respectively.  Of  the  second  winding, 
each  set  of  coils  C  and  C  and  D  and  D'  is  equally  distant 
from  the  position  of  maximum  action,  and  these  two  sets 
are,    therefore,    connected    in    parallel    with    each    other 


1954  APPLIED   ELECTRICITY. 

through  brushes  ^  and  >^',  which  rest  on  segments  c  and  d, 
and  brushes  S  and  <?',  which  rest  on  segments  c'  and  d\  and 
are  connected  in  series  with  the  set  of  coils  B  and  B'  by  the 
external  connection  between  the  two  sets  of  brushes  2  and 
2'  and  3  and  S\ 

To  follow  out  the  changes  in  the  connections  of  the  coils^ 
consider  that  the  armature  is  moving  in  the  direction 
indicated  by  the  arrow. 

As  coils  B  and  B'  move  away  from  their  position  of 
maximum  action,  brushes  1'  and  2'  are  disconnected  from 
segments  b  and  b\  and  as  the  armature  moves,  finally  come 
into  contact  with  segments  a  and  «',  thus  throwing  the  two 
sets  of  coils  A  and  A'  and  B  and  B'  in  parallel.  At  the  same 
time,  brushes  ^  and  S  being  disconnected  by  the  insulating 
segments  from  segments  c  and  d^  only  coils  D  and  D'  of  the 
second  winding  are  connected  to  the  circuit  through  brush 
4'  and  in  series  with  the  coils  of  the  other  winding  (now 
connected  in  parallel)  through  brush  S'  and  its  connection 
with  brushes  2  and  2\  coils  C  and  C  being  entirely  dis- 
connected. 

It  will  be  seen  that  these  successive  combinations  of  coils 
are  precisely  the  same  as  take  place  in  the  Brush  machine, 
except  that  each  combination  takes  place  six  times  in  each 
revolution  instead  of  twice,  due  to  the  multipolar  field. 


CLOSED-COIL  BIPOLAR  ARMATURES. 

3094.  The  greater  part  of  the  applications  of  the 
electric  current  demands  that  the  current  shall  not  only  be 
direct,  i.  e.,  unchanging  in  direction,  but  continuous,  i.  e., 
maintaining  a  constant  voltage.      (See  Art.  3056.) 

Of  the  two  types  of  direct-current  armatures  considered, 
the  unipolar  is  limited  in  its  application  by  reason  of  the 
impossibility  of  coiling  its  conductors;  in  the  open-coil  type 
this  difficulty  does  not  exist,  but  in  order  to  avoid  serious 
pulsations  in  the  current  output,  it  is  necessary  to  use  a 
large  number  of  armature   windings,  each  with  its  com- 


APPLIED   ELECTRICITY.  1955 

mutator   and    brushes,   which    soon    leads    to    undesirable 
complication  in  the  construction. 

3095.  It  is  easily  seen  that  with  bipolar  or  multipolar 
induction,  it  is  necessary  to  employ  some  form  of  commuta- 
tor in  order  to  obtain  a  direct  current  in  the  external  circuit, 
since  the  E.  M.  F.  induced  in  the  coils  of  the  winding  is 
alternating;  further,  to  obtain  a  practically  continuous  cur- 
rent, it  is  evident  that  a  considerable  number  of  coils  must 
be  used,  and  the  number  of  active  coils  that  are  connected 
between  the  brushes  must  be  as  nearly  as  possible  the  same, 
and  connected  in  the  same  manner,  in  all  parts  of  a  revolu- 
tion, and  not  alternately  connected  in  parallel  and  in  series 
with  other  coils,  or  disconnected  entirely  from  the  circuit, 
as  in  the  open-coil  windings.  In  order  to  maintain  this 
equality  in  the  number  and  connections  of  the  coils,  they 
must  be  connected  in  series  with  one  another,  otherwise 
their  unequal  E.  M.  F.'s  would  give  rise  to  wasteful  local 
currents.  This  being  the  case,  and  in  order  that  the  con- 
nection between  any  particular  coil  and  the  external  circuit 
be  reversed  as  the  E.  M.  F.  of  the  coil  is  reversed,  i.  e. ,  as 
the  coil  passes  through  the  neutral  space,  without  discon- 
necting the  coil  altogether  from  the  circuit,  it  is  necessary 
that  both  of  the  commutator  segments  to  which  it  is 
attached  should  come  in  contact  with  the  same  brush  at 
the  time  the  coil  is  in  the  neutral  space;  that  is,  the  coil 
must  be  short-circuited  by  the  brush. 

3096.  In  the  windings  illustrated  in  Fig.  1149,  two 
separate  coils  are  connected  between  each  pair  of  commuta- 
tor segments,  the  coils  being  connected  in  series.  It  is 
evident,  however,  that  each  separate, coil  may  be  supplied 
with  a  two-segment  commutator,  as  represented  in  Fig.  1158. 

Here,  as  in  Fig.  1149,  the  four  coils  are  represented  at  A, 
A',  B,  and  B',  and  each  coil  is  connected  to  a  commutator 
of  two  segments,  coil  A  to  segments  a  and  a,  etc. 

This  results  in  four  commutators  (which  are,  for  con- 
venience, represented  as  being  concentric,  as  before),   upon 


1056 


APPLIED   ELECTRICITY. 


each  of  which  rests  a  pair  of  brushes,  1,  2,  3,  and  Jf,  repre- 
senting the  —  brushes  and  i',  ^',  3\  and  J/  the  +  brushes. 
Since  in  the  ring  winding  coils  A  and  B  are,  respectively, 
diametrically  opposite  coils  A'  and  B' ,  and  in  the  drum 
winding  the  same  coils  practically  coincide  in  position,  it  is 
evident  that  the  E.  M.  F.'s  of  each  of  these  pairs  {A  and  B 
and  A'  and  B')  will  be  the  same,  although  the  E.  M.  F.'s  of 
the  individual  coils  may  differ  in  different  parts  of  the 
revolution.  Consequently,  the  winding  may  now  be  con- 
nected up   (by  suitable  external  connections  between    the 


Fig.  n58. 

brushes)  so  that  coils  A  and  B  and  A'  and  B'  will  be  in 
series,  while  the  two  pairs  oi  coils  are  in  parallel.  This  con- 
dition is  represented  in  Fig.  1158,  coils  A  and  B  being  con- 
nected in  series  by  the  connection  between  brushes  1'  and  2, 
and  coils  A'  and  B'  being  similarly  connected  in  series  by  the 
connection  between  brushes  3  and  Jf.  The  two  pairs  of 
coils  are  connected  in  parallel  by  connecting  together 
brushes  1  and  ^  and  brushes  2'  and^',  these  pairs  of  brushes 
then  serving  as  the  terminals  -f-  and  —  of  the  external 
circuit. 


3097.  From  the  above  it  follows  that  there  are  two 
paths  for  the  current  in  passing  through  the  armature;  in 
the  position  shown  in  the  figure,  one  of  these  is  from  brush 
7,  through  coil  B  to  brush  i',    thence   through  the  external 


APPLIED   ELECTRICITY.  1957 

connection  to  brush  i2,  thence  through  coil  A  and  out 
through  brush  2'.  The  other  is  from  brush  ^,  through  coil 
A'  to  brush  ^',  tlience  through  the  external  connection  to 
brush  3,  thence  through  coil  B'  and  out  through  brush  3'. 

As  the  armature  revolves  (in  the  direction  indicated  by 
the  arrows),  coils  B  and  B'  approach  the  neutral  position, 
and  when  their  E.  M.  F.'s  are  reduced  to  zero,  they  are  mo- 
mentarily short-circuited  as  brushes  1  and  1'  and  3  and  ^' 
bridge  over  the  gaps  between  the  ends  of  segments  /;  and  b 
and  b'  and  b' .  Immediately  after  they  are  again' connected 
in  circuit,  but  in  the.  opposite  direction,  so  that  the  E.  M.  F, 
generated  in  them  as  they  pass  under  the  5"  pole  still  adds  to 
the  E.  M.  F.  acting  on  the  external  circuit. 

3098.  It  will  be  seen  that  this  winding  fulfils  some  of 
the  conditions  laid  down  in  Art.  3095,  namely,  that  the 
connections  between  the  coils  are  not  disturbed  throughout 
a  revolution,  and  that  the  connections  between  a  coil  and 
the  external  circuit  are  reversed  as  there  described. 

There  is  not  a  sufficiently  large  number  of  armature  coils 
to  give  anything  but  a  pulsating  current,  and  any  increase 
in  the  number  of  armature  coils,  and,  consequently,  com- 
mutators, would  lead  to  a  very  complicated  and  undesirable 
construction,  if  arranged  in  the  same  manner  as  those  al- 
ready used. 

However,  as  the  external  connections  between  the  various 
brushes,  (in  Fig.  1158)  serve  to  connect  certain  commutator 
segments  together,  these  segments  might  be  permanently 
connected  without  affecting  the  action  of  the  armature  when 
in  the  position  shown  in  Fig.  1158,  and  only  two  brushes 
would  then  be  required,  as  iand^'.  Under  these  conditions 
the  commutator  would  have  but  four  pairs  of  segments,  the 
segments  of  each  pair  again  forming  practically  one  seg- 
ment. Thus,  these  four  segments  could  be  made  in  the  form 
of  a  single  four-segment  commutator,  as  represented  in  Fig. 
1159. 

3099.  In  this  new  arrangement  each  segment  of  the 
commutator  is  made  up  of  two  of  the  segments  shown  in  tne 


1958 


APPLIED   ELECTRICITY. 


original  scheme.     These  parts  have  been  lettered   to  corre- 
spond with  the  segments  shown  in  Fig.  1158. 

Further,  as  will  be  seen  by  comparing  the  two  figures, 
these  parts  of  the  original  segments  are  so  located  that  the 
brushes  {1  and  2,  Fig.  1159)   bridge  over   the  gap  between 


FIG.  1159. 

them  at  exactly  the  same  part  of  the  revolution  as  the 
terminal  brushes  (the  brushes  connected  directly  to  the  ex- 
ternal circuit,  1  and  Jf.  and  2'  and  S' ,  Fig.  1158)  in  the  origi- 
nal scheme  shown  in  Fig.  1158,  and  the  connections  made 
by  the  intermediate  brushes  {2  and  3  and  1'  and  4',  Fig. 
1158)  are  replaced  by  the  permanent  connections  between 
the  two  parts  of  a  segment. 

The  action  of  this  new  arrangement  is  then  identical  with 
that  shown  in  Fig.  1158,  since  the  coils  are  connected  di- 
rectly to  the  brushes,  short-circuited  when  in  the  neutral 
space,  etc.,  at  exactly  the  same  part  of  the  revolution  and 
in  the  same  manner. 

3100.  In  order  to  more  clearly  show  the  similarity  of 
the  two  methods,  the  brushes  have  been  shown  in  the  same 
position  relative  to  the  pole-pieces  in  each  figure,  the  only  re- 
quirement in  this  respect  being  that  the  coils  shall  be  short- 
circuited  by  the  brushes  when  in  the  neutral  space.  The 
connections  between  a  coil  and  its  commutator  segments 
can  be  so  carried  out  that  the  brushes  may  have  any  posi- 
tion with  respect  to  the  pole-pieces. 


APPLIED   ELECTRICITY. 


1959 


Thus,  in  the  ring  winding  shown  in  Fig.  1159,  the  com- 
mutator and  the  brushes  may  be  moved  bodily  around  to 
the  left  until  each  of  the  gaps  between  the  commutator  seg- 
ments stands  opposite  the  coil  which  is  connected  across  the 
gap,  which  would  materially  lessen  the  length  of  the  connec- 
tions between  the  coils  and  the  commutator,  and  the  brushes 
would  then  rest  at  the  ends  of  the  vertical  diameter  instead 
of  the  horizontal,  as  at  present.  In  the  case  of  the  drum 
winding,  the  connections  between  the  ends  of  a  coil  and  the 
commutator  segments  are  now  of  equal  length,  so  that  any 
change  in  the  position  of  the  commutator  would  only  result 
in  shortening  one  connection  and  lengthening  the  other. 

31  Ol.  This  new  arrangement  is  still  open  to  the  objec- 
tion of  having  too  few  coils,  but  it  will  be  evident  from  an 
inspection  of  Fig.  1159  that  to  increase  the  number  of  coils 
it  is  only  necessary  to  divide  each  segment  in  the  middle 
and  connect  a  new  coil  across  the  gap  so  formed.  The 
effect  of  this  is  shown  in  Fig.  1160,  which  represents  the 


7^7777777^^777777 


Fig.  1160. 


same  windings  as  Fig.  1159,  with  four  new  coils  C,  C,  D, 
and  D'  inserted  in  each.  In  the  case  of  the  ring  winding 
the  commutator  and  brushes  have  been  turned  to  the  left  to 
bring  the  segments  to  which  a  coil  is  connected  directly 
opposite  the  coil.  In  the  drum  winding  the  position  of  the 
commutator  and  brushes  remains  unchanged. 


1960  APPLIED   ELECTRICITY. 

31 02.  From  an  examination  of  Fig.  1160,  it  will  be  seen 
that  there  are  two  leads  (pronounced  leeds)  connected 
to  each  commutator  segment;  that  is,  the  segment  a  c  has 
the  two  leads  c  C  and  a  A. 

It  is  evident,  however,  that  instead  of  connecting  a  lead 
from  each  coil  directly  to  the  commutator,  the  coils  may  be 
connected  directly  together,  and  a  single  wire  run  from  this 
connection  down  to  the  corresponding  commutator  segment. 
In  this  case  the  current  would  traverse  the  commutator 
segment  only  during  the  time  that  the  segment  is  in  contact 
with  a  brush. 

The  result  of  this  arrangement  is  that  the  winding  itself 
forms  a  continuous  spiral  around  the  armature  core,  with 
the  end  joined  to  the  beginning;  that  is,  the  winding  is 
reentrant,  or  closed  iLpon  itself.  From  this  feature,  this 
form  of  winding,  whether  applied  to  a  ring  or  a  drum  core, 
is  called  a  closed-coil  Avinding.  Having  the  closed  coil 
wound  upon  the  core,  the  connections  or  leads  to  the  com- 
mutator segments  may  be  tapped  in  at  convenient  points; 
the  number  of  turns  of  the  winding  which  exist  between  two 
adjacent  points  where  the  leads  to  the  commutator  segments 
are  attached  constitute  an  armature  coil. 

By  winding  the  turns  close  together  on  the  core  so  as  to 
utilize  the  whole  of  its  surface,  and  bringing  out  a  sufHcient 
number  of  leads  to  the  commutator,  a  winding  consisting  of 
a  large  number  of  coils  may  be  obtained. 

31 03.  From  the  nature  of  the  winding,  these  coils  will 
be  equally  divided  into  two  parallel  circuits  around  the 
armature.  Beginning  at  one  brush,  the  current  generated 
passes  from  one  commutator  bar  through  one  lead,  and  splits 
(or,  if  there  be  two  leads  to  each  bar,  splits  at  the  commu- 
tator bar),  passing  on  around  and  around  the  armature  till  it 
finds  an  outlet  through  the  lead  (or  leads)  to  the  commu- 
tator bar  at  the  opposite  side,  and  arrives  at  the  other  brush. 
If  there  is  an  even  number  of  bars,  the  brushes  will  cover 
opposite  bars  at  the  same  instant,  which  means  that  there  is 
an  even  total  number  of  coils,  and  that  each  branch  of  the 


APPLIED   ELECTRICITY.  1961 

circuit  contains  the  same  number  of  coils.  If  there  is  an 
odd  number  of  commutator  bars,  and,  consequently,  an  odd 
number  of  coils,  the  instant  when  one  brush  makes  con- 
tact with  one  bar  the  opposite  brush  makes  contact  with 
two  bars,  thus  cutting  one  coil  out  of  action  for  the 
time  being,  which  leaves  as  before  an  equal  number  of  coils 
in  each  circuit  of  the  armature.  As  the  brushes  pass  on 
from  bar  to  bar,  in  either  case,  it  is  seen  that  the  brush 
must  touch  two  bars,  and  thus  short-circuit  a  coil,  or  cut  it 
out  of  action.  For  this  reason  the  number  of  coils  employed 
in  generating  the  current  will  not  be  constant,  and,  conse- 
quently, the  voltage  will  vary.  This  variation  is  very  slight, 
however,  when  the  number  of  coils  is  high,  and  is  of  no 
material  importance. 

The  E.  M.  F.  of  each  half  of  the  armature  winding  is  made 
up  of  the  sum  of  all  the  E.  M.  F.'s  generated  in  the  separate 
conductors  that  are  connected  in  series  between  the  brushes, 
and  as  the  various  commutator  segments  are  connected  to 
the  winding  at  successive  intervals,  the  difference  of  poten- 
tial between  the  brushes  rises  in  a  series  of  steps  froipi  the 
negative  to  the  positive  brush,  the  difference  of  potential 
between  adjacent  segments  being  equal  to  the  E.  M.  F. 
generated  in  the  coil  which  is  connected  between  them. 
The  greatest  difference  of  potential  between  adjacent  seg- 
ments is,  therefore,  in  the  forms  of  winding  so  far  considered, 
only  equal  to  the  maximum  E.  M.  F.  that  is  generated  in  a 
single  coil. 

CALCULATION    OF    E.  M.  F. 

31 04.  Although  at  any  instant  the  E.  M.  F.'s  of  all  the 
separate  conductors  may  be  quite  different,  owing  to  vari- 
ations in  the  density  of  the  field,  the  sum  of  all  the  separate 
E.  M.  F.'s  is  practically  constant.  It  is  only  necessary,  then, 
to  calculate  the  average  E.  M.  F.  in  each  conductor,  and  to 
multiply  this  average  E.  M.  F.  by  the  number  of  conductors 
connected  in  series  to  obtain  the  E.  M.  F.  of  the  armature. 

Let  N  =.  the  total  number  of  lines  of  force  that  emanate 
from  one  pole-piece  and  are  cut  by  the  conductors;    then, 


1962  APPLIED   ELECTRICITY. 

each  conductor  cuts  2  iV  lines  of  force  per  revolution,  since 
it  cuts  each  line  twice.  Let  5  =  the  number  of  revolutions 
per  minute  of  the  armature ;  then,  the  average  rate  at  which 

each  conductor  cuts  the  lines  of  force  is  ■ — — -—  lines  of  force 

per    second.     The   average   E.  M.  F.,  r,   generated    in    each 

"INS        ^  ,  ,  , 

conductor  is,  then,  e  =  — — -.      Let  c  —  the  total  number 

^  of  conductors  on  the  surface  of  the  armature ;  then,  in  each 

an  E.  M.  F.  =  ^  is  generated,  but  in  only  —  conductors  are 

these  E.  M.  F.'s  added,  since  the  conductors  are  arranged  in 
two  parallel  circuits.  The  total  E.  M.  F.  generated  in  the 
armature  E  is,  then, 

„ -     c  2NS 

E  =  ^  X 


2        60  X  10' 

It  will  be  seen  from  the  above  that  the  fact  that  each  con- 
ductor cuts  the  lines  of  force  twice  is  balanced  by  the  fact 
that  only  half  the  conductors  are  in  series,  so,  by  canceling 
the  2's,  the  formula  becomes 

From  this  formula,  having  given  any  three  of  the  four 
quantities,  E,  c,  N,  and  5,  the  fourth  may  be  readily  found. 


COMMUTATIOIV   OF    CURRENT. 

31 05.  From  Fig.  1160  it  will  be  seen  that  although  a 
coil  when  approaching  the  middle  of  the  neutral  space  may 
have  little  or  no  E.  M.  F.  generated  in  it,  it  must  carry  the 
entire  current  which  is  flowing  in  the  part  of  the  armature 
in  which  it  is  included,  until  the  following  segment  of  the 
pair  to  which  it  is  connected  comes  into  contact  with  a 
brush,  which  allows  the  current  from  that  part  of  the  arma- 
ture to  flow  through  the  brush  without  passing  through  the 
coil  under  consideration.     When  the  leading  segment  of  the 


APPLIED   ELECTRICITY.  1963 

pair  to  which  the  coil  is  connected  passes  out  from  under  the 
brush,  the  coil  is  again  inserted  in  the  armature  circuit,  but 
in  the  other  side,  so  that  the  current  flowing  through  it  is  in 
the  opposite  direction.  From  this  it  follows  that  the  current 
in  the  coil  must  be  reversed  in  direction  during  the  time 
that  a  brush  is  resting  on  botJi  of  the  segments  to  which  the 
coil  is  connected.  Since  the  coil,  whether  of  the  ring  or  the 
drum  winding,  consists  of  one  or  more  turns  of  wire  wrapped 
around  an  iron  core,  its  inductance  is  an  appreciable  quan- 
tity;  hence,  when  the  coil  is  short-circuited  by  the  brush,  the 
current  does  not  immediately  drop  to  zero,  but  continues  to 
circulate  through  the  local  circuit  formed  by  the  coil,  the 
two  commutator  segments,  and  the  brush,  it  being  main- 
tained by  the  self-induced  E.  M.  F.  of  the  coil. 

3106.  Further,  when  the  leading  segment  of  the  coil 
passes  out  from  under  the  brush  and  introduces  the  coil  into 
the  armature  circuit  again,  the  inductance  of  the  coil  will 
tend  to  prevent  the  current  in  it  from  suddenly  attaining  the 
same  value  as  that  flowing  in  the  part  of  the  armature  cir- 
cuit into  which  the  coil  is  introduced.  The  result  of  this 
action  is  that  the  apparent  resistance  of  the  coil  is  very 
largely  increased  at  that  time,  so  that  only  a  part  of  the 
current  passes  through  the  coil  to  the  brush  when  the  lead- 
ing segment  of  the  coil  first  passes  out  from  under  it,  but, 
instead,  continues  to  flow  directly  between  the  leading  seg- 
ment and  the  brush  through  the  narrow  air-space  that  sepa- 
rates them,  thus  causing  a  spark.  As  this  distance  gets 
greater,  more  and  more  of  the  current  flows  around  through 
the  coil  which  has  been  short-circuited,  and  the  spark  be- 
comes less  and  less  intense,  and  finally  disappears.  All  these 
operations  take  only  a  very  short  time,  usually  about  as  long 
as  is  required  for  the  armature  to  rotate  through  the  angle 
embraced  by  one  or  two  commutator  segments,  so  that  the 
spark  lasts  only  a  small  fraction  of  a  second;  but  as  it  is 
repeated  at  every  brush  for  every  coil  that  is  short-circuited, 
the  aggregate  result  is  that  the  sparking  eats  away  both 
brushes  and  commutator  segments,  thus  causing  a  consider- 


1964  APPLIED   ELECTRICITY. 

able  deterioration  of  the  machine,  besides  wasting  a  certain 
amount  of  energy. 

3107.  If  an  E.  M.  F,  is  introduced  into  the  local  circuit 
(formed  by  the  coil,  its  commutator  segments,  and  the 
brush),  which  is  opposite  in  direction  to  the  E.  M.  F.  of  self- 
induction,  not  only  may  the  current  in  the  coil  be  brought 
more  quickly  to  zero,  but  it  may  even  be  reversed  and 
caused  to  flow  in  the  opposite  direction,  while  the  coil  is  still 
short-circuited  by  the  brush.  Evidently,  then,  if  this  re- 
verse current  is  brought  up  to  the  same  value  as  that  flow- 
ing in  the  part  of  the  armature  into  which  the  coil  is  inserted 
at  the  moment  the  brush  leaves  the  leading  segment,  there 
is  no  change  in  the  amount  or  direction  of  the  current  flow- 
ing in  the  coil,  consequently  no  sparking  as  commutation  is 
effected. 

If  the  value  of  the  reverse  current  in  the  short-circuited 
coil  at  the  moment  the  brush  leaves  the  leading  segment  is 
less  than  the  current  it  will  have  to  carry,  the  spark  will 
occur  as  before,  but  to  a  much  less  degree,  since  the  amount 
of  change  in  the  current  of  the  coil  is  much  less,  conse- 
quently its  E.  M.  F.  of  self-induction  and  its  apparent  re- 
sistance are  much  reduced;  if  the  current  in  the  coil  is 
greater  than  that  which  it  is  to  carry,  the  excess  of  current 
can  not  immediately  disappear  as  the  brush  leaves  the  lead- 
ing segment,  owing,  as  before,  to  the  inductance  of  the  coil, 
but  continues  to  flow,  the  local  circuit  now  including  the 
small  air-space  between  the  leading  segment  and  the  top  of 
the  brush.  In  other  words,  sparks  appear  at  the  brushes, 
as  before. 

31 08.  Fig.  1161  illustrates  both  these  conditions,  rep- 
resenting a  section  of  a  ring  armature  with  the  coils  «,  b, 
c\  d,  and  e  and  the  corresponding  commutator  segments. 
In  each  figure  {A  and  B)  each  half  of  the  armature  winding 
is  supposed  to  have  flowing  in  it  10  amperes,  as  indicated  by 
the  numbers  near  the  arrows  that  show  the  direction  of  the 
current.  In  each  figure,  coil  c  is  represented  as  just  passing 
out  of  the  condition  of  short  circuit,  i.  e.,  the  brush  (T  is  just 


APPLIED   ELECTRICITY. 


1965 


leaving  the  leading  segment  of  coil  c.  \n  A,  coil  c  is  sup- 
posed to  have  an  E.  M.  F.  acting  in  it  which  is  sufficient  to 
reverse  the  current  and  bring  it  up  to  a  value  of  5  amperes 
at  the  instant  its  short  circuit  is  broken,  so  that  at  that  in- 
stant, owing  to  the  inductance  of  the  coil,  only  5  amperes  of 
the  main  current  can  flow  through  the  coil,  the  balance 
passing  through  the  tiny  air-space  from  the  leading  segment 
to  the  tip  of  the  brush  67,  as  represented.  In  i?,  the  E.  M.  F. 
ah  Q,  h 


Fig.  1161. 
acting  in  coil  c  is  supposed  to  be  great  enough  to  bring  the 
current  in  the  coil  up  to  15  amperes,  so  that  when  the  brush 
leaves  the  leading  segment  the  15  amperes  continue  to  flow 
for  an  instant,  10  being  supplied  by  the  half  of  the  armature 
into  which  the  coil  is  connected,  and  the  other  5  passing 
across  the  tiny  air-space  from  the  tip  of  the  brush  C  to  the 
leading  segment  of  the  coil,  as  represented. 

Of  course,  this  condition  of  affairs  lasts  for  only  a  moment, 
the  current  in  coil  c  quickly  adjusting  itself  to  the  armature 
current  (10  amperes  in  this  case). 

3109.  The  E.  M.  F.  necessary  to  reverse  the  current 
in  the  coil  may  be  supplied  in  a  variety  of  ways.  It  will  be 
seen  that  the  direction  of  this  E.  M.  F.  must  be  the  same 
as  that  generated  in  the  coils  of  the  part  of  the  armature 
circuit  into  which  the  coil  is  to  be  introduced.  Conse- 
quently, by  moving  the  brush  aJicad^  i.  e.,  in  the  direction 
of  rotation  of  the  armature,  until  the  coil,  when  short-cir- 
cuited, is  in  the  magnetic  field,  the  necessary  E.  M.  F.  will 
be  generated  in  the  coil.     When  the  armature  is  furnishing 


1966  APPLIED   ELECTRICITY. 

a  very  small  current,  the  E.  M.  F.  required  to  reverse  the 
current  in  the  short-circuited  coil  will  be  comparatively 
small,  and  as  the  current  output  of  the  armature  increases, 
this  E.  M.  F.  will  have  to  be  similarly  increased.  There  is 
no  abrupt  change  from  the  neutral  space  to  the  magnetic 
field ;  that  is,  at  the  edge  of  the  field  the  density  of  the  lines 
of  force  gradually  shades  off  to  zero  in  the  neutral  space. 
Consequently,  when  only  a  small  current  is  flowing  in  the 
armature,  it  is  not  necessary  to  push  the  brushes  ahead 
very  far  to  move  the  short-circuited  coil  into  a  field  of  suf- 
ficient strength  to  supply  the  necessary  E.  M.  F.  during  the 
period  of  short  circuit ;  as  the  current  in  the  armature  in- 
creases, however,  it  is  necessary  to  move  the  brushes  ahead 
still  farther,  in  order  that  the  field  in  which  the  coil  moves 
while  short-circuited  may  be  of  sufficient  density  to  supply 
the  necessary  E.  M.  F.  for  reversing  the  current. 

This  movement  of  the  brushes  is  usually  obtained  by 
mounting  the  holders  for  the  several  brushes  on  a  common 
support  that  can  be  made  to  turn  around  the  axis  of  the 
armature  and  be  clamped  in  any  desired  position.  By  rota- 
ting this  support,  the  brushes  are  simultaneously  moved  to 
the  desired  position,  as  evinced  by  the  cessation  of  the 
sparking  whenever  a  change  in  the  current  calls  for  such 
an  adjustment. 

3110.  Another  method  of  introducing  an  E.  M.  F.  into 
the  short-circuited  coil  results  from  the  fact  that  the  local 
circuit  through  which  the  current  in  the  short-circuited  coil 
flows  is  in  part  through  the  brush.  In  addition,  the  current 
from  both  parts  of  the  armature  winding  also  flows  through 
the  same  two  commutator  segments  into  the  brush.  It  is 
evident,  then,  that  as  the  leading  segment  passes  out  from 
under  the  brush,  the  area  of  brush  surface  that  is  in  contact 
with  this  segment  grows  rapidly  less,  thus  increasing  the 
resistance  in  the  path  of  the  current  that  is  flowing  from  the 
part  of  the  armature  circuit  into  which  the  short-circuited 
coil  is  about  to  be  inserted.  If  the  brush  is  made  of  a 
material  of   high  conductivity,   this  increase  in   the  resist- 


APPLIED   ELECTRICITY.  1967 

ance  will  be  slight,  and  will  produce  little  or  no  effect  until 
the  leading  segment  is  actually  leaving  the  brush;  but  if 
of  comparatively  low  conductivity,  the  increase  in  the  re- 
sistance will  be  more  pronounced,  and  will  cause  a  drop,  or 
difference  of  potential,  between  the  commutator  segment 
and  the  brush.  The  other  segment,  however,  is  all  the  time 
moving  more  and  more  under  the  brush,  thus  reducing  the 
resistance  at  that  point,  so  that  the  difference  of  potential 
between  the  leading  segment  and  the  brush  tends  to  send 
the  current  around  through  the  short-circuited  coil  and  into 
the  brush  through  the  other  segment. 

31 11.  In  other  words,  this  difference  of  potential  acts 
as  an  E.  M.  F.  to  reverse  the  current  in  the  short-circuited 
coil;  consequently,  it  will  prevent  sparking  just  as  setting 
up  an  E.  M.  F.  in  the  coil  itself  will,  if  of  the  right  amount. 
It  will  be  seen  that  as  the  current  in  the  armature  increases, 
thus  requiring  a  greater  E.  M.  F.  to  reverse  the  current  in 
the  short-circuited  coil,  the  difference  of  potential  between 
the  leading  segment  and  the  brush  also  increases  at  the  same 
rate,  so  that  this  method  of  preventing  sparking  is,  to  some 
extent,  self-regulating.  However,  this  method  by  itself  can 
not  well  be  used,  as  it  is  impracticable  to  so  adjust  the 
nature  and  extent  of  the  contact  surface  of  the  brush  as  to 
obtain  the  right  E.  M.  F.  for  reversing  the  current;  and 
even  if  this  adjustment  were  once  made,  it  could  not  be 
permanent,  owing  to  changes  in  the  extent  and  nature  of 
the  contact  surface  of  the  brush  and  its  variations  in  pressure 
incident  to  the  continual  operation  of  the  machine,  the 
amount  of  the  contact  resistance  depending  upon  all  of 
these  factors. 

3112.  In  practice,  commutation  is  effected  by  a  com- 
bination of  these  two  methods;  that  is,  the  brushes  are 
shifted  until  the  E.  M.  F.  induced  in  the  short-circuited  coil, 
aided  by  the  difference  of  potential  between  brush  and  seg- 
ment, is  sufficient  to  ensure  sparkless  commutation.  With 
metallic  brushes,  the  contact  resistance  is  usually  so  low  as 
to  render  the  difference  of  potential  between  the  brush  and 


1968  APPLIED    ELECTRICITY. 

segment  of  very  little  value  in  commuting  the  current.  In 
other  words,  the  E.  M.  F.  induced  in  the  coil  itself  must  do 
the  reversing;  hence,  the  brushes  must  be  newly  shifted  for 
each  small  change  in  the  current  output  to  proportionately 
change  the  E.  M.  F.  acting  in  the  short-circuited  coil. 
With  brushes  of  higher  resistance,  however,  the  difference 
of  potential  developed  at  the  contact  surface  furnishes  such 
a  large  proportion  of  the  total  E.  M.  F.  required  that  the 
brushes  may  remain  in  one  position  during  considerable 
changes  in  the  current  output.  High-resistance  brushes, 
therefore,  require  less  shifting  to  obtain  sparkless  commu- 
tation than  do  those  of  low  resistance. 

3113.  It  will  be  seen  that  to  commute  a  given  current 
in  a  given  length  of  time,  the  E.  M.  F.  required  will  be 
proportional  to  the  inductance  of  the  armature  coil.  Con- 
sequently, it  is  desirable  that  the  armature  coils  have  as 
little  inductance  as  possible,  since  there  will  then  be  less 
E.  M.  F.  required  to  commute  the  current;  or,  in  other 
words,  there  will  be  less  shifting  of  the  brushes  necessary 
for  sparkless  commutation. 

From  the  very  nature  of  the  factor,  it  is  evident  that  as 
the  armature  coils  are  wound  on  an  iron  magnetic  circuit, 
they  must  be  of  few  turns  in  order  that  their  inductance 
may  be  low;  consequently,  the  winding  should  be  divided 
into  as  many  coils  as  convenient,  thus  making  the  number 
of  commutator  segments  comparatively  large. 

3114.  There  are  other  considerations  which  influence 
the  number  of  commutator  segments  to  be  used  in  any  par- 
ticular case;  for  example,  if  the  maximum  difference  of 
potential  between  adjacent  commutator  segments  is  20  volts 
or  greater,  any  sparking  at  the  tip  of  the  brush  is  liable  to 
continue  between  the  commutator  segments  as  the  arma- 
ture turns;  as  each  segment  passes  out  from  undeif  t-he 
brush  a  similar  arc  may  be  maintained,  until  they  all  extend 
from  brush  to  brush,  short-circuiting  the  whole  armature. 
To  prevent  this,  the  average  difference  of  potential  between 
the  segments  should  not  be  greater  than  about  15  volts,  if 


APPLIED   ELECTRICITY. 


1969 


the  machine  is  to  give  a  current  of  more  than  about  20  am- 
peres. With  less  current  output,  a  greater  average  differ- 
ence of  potential  may  be  used  if  necessary. 


ARMATURE   REACTION. 

31 15.  It  has  been  discussed  and  shown  previously  that 
when  a  current  is  flowing  in  a  conductor  located  in  a  mag- 
netic field  a  reaction  exists  between  the  current  and  the 
field,  so  that  a  force  must  be  applied  to  the  conductor  in 
order  to  move  it  through  the  field.  This  motion  being  op- 
posed by  the  lines  of  force  of  the  field,  the  force  applied  to 
the  conductor  ultimately  acts  on  the  lines  of  force  of  the 
field,  tending  to  crowd  them  ahead  in  the  direction  that  the 
conductor  is  moved.  Consequently,  when  a  current  is  flow- 
ing in  the  conductors  of  a  dynamo  armature  (either  ring  or 
drum  wound),  the  lines  of  force  are  crowded  around  in  the 
direction  of  rotation,  thus  causing  the  field  to  be  less  dense 
under  the  leading  pole  tips,  i.  e. ,  the  pole  tips  towards  which 
coils  that  are  in  neutral  spaces  are  moving,  and  to  be 
more  dense  under  the  following  pole  tips,  than  would  be  the 
case  were  the  field  symmetrically  distributed.  This  is  in- 
dicated in  Fig.  1162,  in  which  an  armature  core  situated  in 
a  bipolar  field  is  repre- 
sented, with  the  conductors 
equally  spaced  around  its 
periphery;  these  conduct- 
ors are  supposed  to  be  con- 
nected up  as  a  closed-coil 
winding,  either  ring  or 
drum,  and  a  current  is  sup- 
posed to  be  flowing  in  the 
winding.  By  applying  the 
thumb-and-fingers  rule  to 
this  figure,  it  will  be  seen 
that  the  direction  of  the 
current  in  the  conductors 
under  the  A^  pole  is  up,  through  the  paper,  while  under  the 


1970 


APPLIED   ELECTRICITY. 


vS  pole  the  current  is  in  the  opposite  direction.  This  is  indi- 
cated by  marking  the  conductors  with  a  -J-  and  a  soHd  black 
dot,  respectively. 

The  relative  distribution  of  the  lines  of  force  is  indicated 
by  the  lines  from  the  pole-pieces  to  the  core;  their  distribu- 
tion within  the  armature  core  is  immaterial  at  present.  It 
will  be  noticed  that  the  effect  of  the  distortion  of  the  field  is 
to  alter  the  relative  density  of  the  lines  of  force  under  the 
pole  tips,  and  to  shift  the  true  neutral  line  {x  y)  from  its 
theoretical  position  half  way  between  the  pole  tips  (line  a  b) 
in  the  direction  of  rotation. 

31 16.     It  does  not  matter  how  the  conductors  are  joined 
together,  so  long  as  the  current  in  each  conductor  is  as  rep- 
„,  resented.         Consequently, 

supposing  the  armature  to 
be  stationary,  the  same 
shifting  of  the  field  would 
result  if  the  conductors 
were  so  connected  as  to 
form  a  spiral  coil  wrapped 
around  the  core,  with  its 
axis  along  the  line  a  b,  as 
represented  in  Fig.  1163, 
the  brushes  being  on  the 
6  ^""<"""<"""<"-  theoretical  neutral  line  a  b. 
Fig.  1163.  The  magnetizing  force  of 

this  coil  acts  along  the  line  a  b,  that  being  the  axis  of  the 
coil.  It  will  be  seen  that  this  introduces  no  magnetomotive 
force  that  is  opposed  to  the  lines  of  force  passing  through  the 
armature,  since  on  each  side  of  a  line  connecting  the  centers 
of  the  pole  faces  there  are  the  same  number  of  conductors 
carrying  the  current  in  each  direction.  The  only  effect 
of  this  armature  magnetomotive  force  is,  then,  to  distort 
the  field. 


3117.  As  soon,  however,  as  the  brushes  are  shifted 
ahead  to  effect  sparkless  commutation,  this  condition  does 
not  hold;  the  shifting  of  the  brushes  introduces  into  that 


APPLIED   ELECTRICITY. 


1971 


part  of  the  armature  that  lies  on  each  side  of  the  center 
line  of  the  pole  faces  an  excess  of  conductors  carrying  a  cur- 
rent in  one  direction,  as  is 
shown  in  Fig.  1164,  which 
represents  an  armature  coil 
in  a  bipolar  field,  with  36 
conductors,  as  before.  It 
is  supposed  in  this  case  that 
the  brushes  are  shifted  un- 
til they  bring  the  short-cir- 
cuited coils  on  the  line  x  y^ 
which  is  ahead  of  the  theo- 
retical neutral  line  a  bhy  the 
angle  r.  From  an  inspec- 
tion of  this  figure,  it  will  be 
seen  that  on   each    side  of  pig.  1164. 

the  center  line  of  the  pole-pieces  the  number  of  conductors 
carrying  the  current  in  one  direction  exceeds  that  of  the 
conductors  carrying  the  current  in  the  opposite  by  the  num- 
ber of  conductors  included  between  the  lines  x  y  and  s  t, 
which  make  equal  angles  with  the  line  a  b.  Further,  it  will 
be  seen  that  the  current  flowing  in  these  conductors  sets  up 
a  magnetomotive  force  which  is  directly  opposed  to  the  mag- 
netic field  in  which  the  armature  revolves.  Hence,  these 
conductors  may  be  considered  as  forming  a  spiral  coil 
around  the  armature,  whose  axis  coincides  with  the  center 
line  of  the  pole-pieces,  as  represented  in  the  illustration, 
Fig.  1164. 


3118.  It  will  be  seen,  then,  that  when  the  brushes  of 
an  armature  are  shifted  ahead  from  the  position  where  the 
short-circuited  coils  are  in  the  theoretical  neutral  line,  in 
order  to  effect  sparkless  commutation,  the  magnetizing 
effect  of  the  armature  current  may  be  divided  into  two  com- 
ponents; one  of  these  acts  in  a  direction  at  right  angles  to 
the  field  in  which  the  armature  revolves,  and  so  distorts  it, 
while  the  other  acts  in  a  direction  opposite  to  the  field, 
hence,   reduces    its  strength.     The    angle  r,    Fig.    1164,   is 


1972  APPLIED   ELECTRICITY. 

evidently  the  angle  through  which  the  brushes  are  shifted; 
hence,  it  is  called  the  angle  of  lead  of  the  brushes.  It  has  been 
shown  that  the  current  in  all  the  conductors  included  in  twice 
the  angle  of  lead  makes  up  the  magnetomotive  force  that 
directly  opposes  the  field,  and  this  is  called  the  counter 
magnetomotive  force  of  the  winding.  It  is  measured 
(in  ampere-turns)  by  the  product  of  the  number  of  conduct- 
ors included  in  twice  the  angle  of  lead  and  the  current 
in  each.  The  current  flowing  in  the  rest  of  the  conductors 
makes  up  the  cross  magnetomotive  force  of  the  wind- 
ing, its  value  in  ampere-turns,  as  before,  being  the  product 
of  the  number  of  conductors  and  the  current  in  each, 

3119.  It  has  been  shown  that  the  brushes  must  be 
shifted  ahead  of  the  neutral  line  in  order  to  bring  the  short- 
circuited  coil  into  a  field  of  sufficient  density  to  set  up  the 
proper  E.  M.  F.  in  it;  it  will  be  seen  that  as  the  armature 
current  increases,  the  density  of  the  field  under  the  leading 
pole  tip  is  decreased  more  and  more,  so  that  the  brushes 
must  be  shifted  farther  to  bring  the  short-circuited  coil 
into  a  field  of  the  proper  density.  This  introduces  a  greater 
and  greater  counter  magnetomotive  force,  which  reduces 
the  strength  of  the  field  still  more,  and  makes  the  effect  of 
the  counter  magnetomotive  force  greater;  and  it  will  be 
readily  seen  that  the  armature  current  might  rise  to  such  a 
value  that  any  amount  of  shifting  of  the  brushes  would  not 
be  sufficient  to  bring  the  short-circuited  coil  into  a  field  of 
sufficient  density  for  sparkless  commutation. 

Thus,  the  armature  reaction  introduces  a  factor  which 
tends  to  limit  the  amount  of  current  which  the  armature 
can  supply,  by  making  an  excessive  shifting  of  the  brushes 
necessary  to  effect  sparkless  commutation,  this  limit  of  load 
being  known  as  the  sparking  limit. 

3l!20.  It  has  already  been  pointed  out  that  force  is 
required  to  move  a  conductor  through  a  magnetic  field 
when  a  current  is  allowed  to  flow  through  the  conductor. 

Applying  this  principle  to  the  armature  winding  of  a 
dynamo,  it  will  be  seen  that  the  current  in  each  conductor 


APPLIED   ELECTRICITY.  1973 

gives  rise  to  a  force  acting  approximately  tangent  to  the 
surface  of  the  armature ;  the  amount  of  the  force  on  each 
conductor  depends  upon  the  strength  of  the  current  in  each 
conductor  and  the  strength  (density)  of  the  field  in  which  it 
lies,  and  the  sum  of  all  these  forces  (in  pounds)  multiplied 
by  the  velocity  of  the  conductors  (in  feet  per  minute)  is  the 
power  (in  foot-pounds  per  minute)  necessary  to  apply  to  the 
conductors  to  move  them  through  the  field  against  the  force 
set  up  by  the  current. 

It  will  be  seen  that  the  calculation  of  the  force  acting  on 
each  conductor  at  any  instant  would  be  difficult,  requiring  a 
knowledge  of  the  density  of  the  field  in  which  each  conduct- 
or is  moving.  But  this  is  not  necessary,  for,  as  has  already 
been  pointed  out  (Art.  3030),  the  power  required  to  move 
the  conductor  is  equal  (when  reduced  to  the  same  units)  to 
the  product  of  the  E.  M.  F.  generated  in  the  conductors  and 
the  current  flowing,  which  are  quantities  readily  measured. 

3121.  The  total  power  required  to  drive  the  armature, 
or  the  input,  is  equal  to  the  power  required  to  drive  the 
conductors,  which  may  be  found  as  pointed  out  above,  plus 
whatever  power  is  necessary  to  overcome  the  friction  of  the 
journals  and  the  hysteresis  and  eddy-current  losses  (see  Arts. 
3050  to  3052)  that  take  place  in  the  armature  core. 
These  quantities  may  be  found  or  calculated  separately  by 
methods  which  will  be  taken  up  later.  It  has  already  been 
shown  that  the  output  of  a  dynamo  is  the  product  of  the 
difference  of  potential  between  its  terminals  and  the  cur- 
rent flowing  in  the  external  circuit;  the  efficiency  of  the 
dynamo  is,  of  course,  the  ratio  between  the  output  and  the 
input. 

CLOSED-COIL   ARMATURE   Ti^INDINGS. 

3122.  Thus  far  only  the  simplest  forms  of  ring  and 
drum  windings  for  bipolar  field-magnets  have  been  con- 
sidered. These  are  susceptible  of  many  modifications,  how- 
ever, especially  when  used  with  multipolar  fields,  some  of 
which  are  essential  for  certain  applications. 


1974 


APPLIED   ELECTRICITY. 


In  the  following  discussion  of  the  most  generally  used 
windings,  for  the  sake  of  simplicity,  only  a  few  conductors 
will  be  represented  in  each  winding,  showing  the  principle 
of  the  winding  and  arrangement  of  the  connections.  The 
conditions  which  govern  the  design  of  a  winding  for  a  com- 
mercial machine  and  the  actual  construction  of  the  winding 
will  be  taken  up  later. 

RING    WINDINGS. 

31 23.  The  simplest  form  of  ring  winding  is  that  already 
described,  in  which  the  conductor  forms  a  continuous  closed 
spiral,  with  leads  ~  brought  out  at  a  series  of  equidistant 
points  to  the  commutator  segments,  and  with  bipolar  fields, 
and  this  form  of  winding  is  not  susceptible  of  much  modi- 
fication. 


Fig.  1165. 


If  a  simple  ring-wound  armature  is  placed  in  a  multipolar 
field,  each  adjacent  pair  of  poles  will  act  on  the  winding  in 


APPLIED   ELECTRICITY.  1975 

the  same  manner  as  a  bipolar  field,  so  that  that  section  of  the 
armature  will  be  divided  into  two  parallel  circuits.  The 
whole  winding  will,  therefore,  be  divided  into  as  many  cir- 
cuits as  there  are  poles,  consequently  requiring  as  many 
brushes.  This  is  represented  in  Fig.  1165,  which  shows  a 
four-pole  field,  with  a  ring-wound  armature  of  32  coils,  each 
of  two  turns.  With  the  larger  number  of,,coils  the  device 
used  as  the  commutator  heretofore,  namely,  metallic  seg- 
ments placed  side  by  side  and  separated  by  air-spaces,  can 
not  be  used  to  advantage ;  instead,  a  large  number  of  seg- 
ments of  approximately  rectangular  section  are  placed  side 
by  side,  separated  by  thin  strips  of  insulating  material. 
This  is  indicated  in  Fig.  1165. 

3124.  It  will  be  seen  that  in  this  arrangement  the 
armature  is  divided  up  into  four  circuits,  and  four  brushes 
are  required,  which  must  be  placed  so  as  to  short-circuit  a 
coil  when  in  the  neutral  space,  as  represented  in  the  figure. 

There  is  no  difference  of  potential  between  the  opposite 
brushes,  +  and  -f-,  or  —  and  — ,  so  that  each  of  these  pairs 
may  be  connected  together  in  parallel,  to  supply  a  single 
external  circuit.  Similarly,  with  6,  8,  10,  or  more  poles,  a 
corresponding  number  of  brushes  must  be  used,  of  which  all 
those  of  like  sign  are  connected  together  in  parallel.  In 
this  form  of  four-pole  armature  (Fig.  1165),  opposite  com- 
mutator bars  are  always  at  the  same  potential ;  consequently, 
there  is  no  difference  of  potential  between  them,  and  they 
may,  therefore,  be  permanently  connected  together.  This 
is  accomplished  by  means  of  cross-connecting  wires,  and 
does  away  with  the  necessity  of  more  than  two  brushes. 
This  can  be  done  only  when  the  winding  is  made  up  of  an 
even  number  of  coils,  for  with  an  odd  number  there  will 
always  be  one  segment  "left  over." 

31 25.  In  general,  with  any  number  of  poles  this  form  of 
winding  has  the  segments  that  are  always  at  the  same  potential 

situated  — — -  apart,  /  being  the  number  of  pairs  of  poles  in 


1976  APPLIED   ELECTRICITY. 

the  field;  and  these  segments  may  be  connected  together  by 
cross-connecting  wires;  only  two  brushes  are  used,  provided 
the  number  of  segments  is  a  multiple  of/. 

3126.  The  E.  M.  F.  generated  in  a  simple  ring  arma- 
ture rotated  in  a  multipolar  field  may  be  found  from  for- 
mula 480,  given  in  Art.  31 04.  The  total  number  of 
cuttings  of  lines  of  force  by  each  conductor  in  one  revolu- 
tion is  2/  A^,  p  being  the  number  oi  pairs  of  poles  and  N  the 
number  of  lines  of  force  that  emanate  from  one  pole  face; 

c 
but  since  only  —  conductors  are  connected   in  series,  the 
2/ 

cNS 
term  2/'  cancels  out,  and  E  =  -- — — — .,  as  before. 
^  '  60  X  10"' 

3127.  Thus  the /t?/«/ number  of  lines  of  force  in  the 
armature  of  a  multipolar  machine  is  equal  to/  N^  p  and  N 
having  the  values  given  above.  Each  line  of  force  is  cut 
twice  by  each  conductor  in  each  revolution,  however,  from 
which  results  the  value  '%  p  N,  given  above. 

The  same  E.  M.  F.  will  be  generated  in  each  of  the  four 
circuits  of  the  winding,  provided  that  the  number  of  lines 
of  force  through  each  gap  space  under  the  poles  is  the  same, 
which  is  usually  the  case,  although,  as  will  be  pointed  out 
later,  it  is  quite  possible  for  it  to  vary. 


TW^O-CIRCUIT   WIIVDIIVGS. 

3128.  If  the  number  of  lines  of  force  through  each  gap 
space  is  not  the  same,  then  the  E.  M.  F.  generated  in  each 
circuit  will  not  be  the  same;  consequently,  the  higher 
E.  M.  F.  of  one  circuit  will  tend  to  make  it  furnish  more 
than  an  equal  share  of  the  current  output  when  connected 
to  the  external  circuit. 

^o  obviate  the  possibility  of  such  an  event  occurring, 
several  systems  of  multipolar  ring  windings  are  in  use,  all 
of  which  are  based  on  the  general  principle  of  connecting 
each  coil  of  the  armature  in  series  Avith  one  which  is  in 
another  field,  of  either  the  same  or  opposite  polarity.  This 
divides  the  armature  winding  into  two  parallel  circuits,  a 


APPLIED  ELECTRICITY. 


1977 


part  of  each  circuit  being  in  two  different  fields,  so  that 
even  if  the  fields  are  individually  not  of  the  same  strength, 
the  E.  M.  F.  of  each  armature  circuit  is  the  same. 

A  winding  which  is  divided  into  only  two  circuits  in 
parallel,  whatever  the  number  of  pairs  of  poles  in  the  field, 
is  known  as  a  two-circuit  winding,  to  distinguish  it  from 
the  form  in  which  the  winding  has  as  many  circuits  in 
parallel  as  there  are  poles,  which  is  called  a  multiple- 
circuit  winding. 

3129.  One  form  of  two-circuit  winding,  in  which  coils 
situated  in  fields  of  like  polarity  are  connected  in  series,  is 


Fig.  1166. 


illustrated  in  Fig.  1166.     A  four-pole  field  is  shown  with  an 
armature  having  17  coils  numbered   from  1  to  17.     Each 


1978  APPLIED   ELECTRICITY. 

coil  is  connected  to  two  commutator  segments,  and  each 
scgmeiit  being  connected  to  two  coils,  there  are,  therefore, 
as  many  segments  as  coils,  i.  e.,  17. 

It  will  be  seen  that  the  cud  of  any  one  coil  is  connected  to 
the  beginning  of  a  coil  which  is  a  certain  number  of  coils 
away  from  it;  for  example,  the  end  of  coil  1  is  connected  to 
the  beginning  of  coil  5,  which  is  9  —1  =  8  coils  to  the  right 
of  coil  1.  This  spacing  is  called  the  pitcli  of  the  winding; 
that  is,  in  the  above  case,  the  pitch  is  8,  and  the  end  of  each 
coil  throughout  the  winding  is  connected  to  the  beginning 
of  the  8th  coil  to  the  right,  as  shown  in  the  figure. 

31 30.  Whether  the  pitch  in  this  form  of  winding  be 
odd  or  even,  in  order  that  all  the  coils  may  be  included  in 
the  winding  before  it  closes  upon  itself,  the  number  of  coils 
must  be  one  more  or  one  less  than  the  product  of  the  pitch  and 
the  number  oi  pairs  of  poles.  Then,  if  /  =  the  number  of 
pairs  of  poles,  y  =  the  pitch,  and  s  =  the  total  number  of 
coils,  in  general, 

s  =  pj;±l.  (481.) 

Thus,  in  the  case  illustrated  in  Fig.  1166,  where/  =  2  and 

J- =  (2  X  8)  ±  1  =  15  or  17. 

In  this  case  17  was  the  number  used,  as  shown.  It  will 
be  seen  from  this  formula  that  when/  is  an  cvc7Z  number,  s 
must  be  an  odd  number ;  while,  if  /  is  odd,  s  may  be  odd  or 
even,  depending  on  whether  jf  is  even  or  odd. 

There  being  but  two  circuits  through  the  armature,  two 
brushes  only  need  be  used,  as  represented. 

Note. — To  prevent  confusion,  the  brushes  have  been  represented  as 
inside  the  commutator  in  this  and  other  figures. 

In  the  position  represented  in  the  figure,  coils  1  and  9  (in 
series)  are  short-circuited  by  the  —brush;  as  the  armature 
continues  to  rotate,  coils  IJ^  and  6  (in  series)  would  next  be 
short-circuited  by  the  -j-brush,  and  so  on. 

3131.  In  general,  the  brushes  for  this  style  of  winding 
may  be  located  as  follows  :    If  one  is  to  the  left  of  a  pole- 


APPLIED   ELECTRICITY. 


1979 


piece,  the  other  must  be  to  the  rigJit  of  a  pole-piece  of  like 
polarity.  In  a  four-pole  machine,  this  allows  of  an  angle 
of  only  90°  between  the  brushes;  but  in  a  six-pole  machine, 
it  allows  of  an  angle  of  either  60°  or  180°,  and  in  an  eight- 
pole  machine  an  angle  of  either  45°  or  135°.  With  a  greater 
number  of  poles,  a  greater  number  of  different  angles  be- 
tween brushes  may  be  used. 

3132.     Another  form  of  two-circuit  ring  winding  is  rep- 
resented  in   Fig.    1167.      Here  the  number  of    coils   is    the 


Fig.  1167. 


same  as  before,  but  twice  the  number  of  commutator  seg- 
ments are  employed.  In  this  case  each  end  of  each  coil  is 
carried  straight  down  to  a  separate  commutator  segment, 
and,   in  addition,   a  cross-connection  is  made  between  each 


1980  APPLIED  'ELECTRICITY. 

commutator  segment  to  the  one  directly  opposite  it.  In 
practice,  it  is  customary  to  place  the  cross-connections  in- 
side the  end  of  the  commutator,  instead  of  between  the  leads 
to  the  commutator,  which  is  the  method  represented  in  the 
diagram. 

Two  brushes  are  used,  located  (with  the  four-pole  field)  90° 
apart  on  the  commutator.  In  the  position  of  the  armature 
represented  in  the  diagram,  coil  9  is  short-circuited  by  the 
-f-brush;  a  moment  later  the  —brush  will  short-circuit  coil 
5,  then  the  -fbrush  will  short-circuit  coil  1,  then  the 
—  brush  will  short-circuit  i^,  and  so  on,  from  which  it  will  be 
seen  that  the  coils  in  the  successive  neutral  spaces  are  short- 
circuited  one  at  a  time. 

3133.  The  formula  for  the  total  number  of  coils  in  the 
winding  given  in  Art.  31 30  (formula  481)  also  applies  to 
this  winding;  but  if  the  direction  of  the  winding  in  the  coils 
is  always  assumed  to  advance  in  the  same  direction  as  the 
numbering  of  the  coils,  so  that  the  end  of  coil  1  adjoins  the 
beginning  of  coil  ^,  and  so  on  (which  is  the  logical  way  of 
considering  it),  then  the  number  of  coils  which  can  be  used 
is  only  that  given  by  the  formula  s  ^^  p y  —  1. 

Thus,  in  Fig.  1167,  /  =  2  and  jK  =  9,  and  .y  =  (2  X  9)  —  1 
=:  17  coils.  If-f-lhad  been  used  instead  of— 1,  the  num- 
ber of  coils  would  have  been  19,  and  a  closed-coil  winding 
would  have  resulted,  but  the  distribution  of  potentials 
between  commutator  segments  would  have  been  very 
irregular,  since  several  coils  would  be  included  between 
adjacent  bars  in  some  instances. 

31 34.  Since  the  object  of  the  cross-connections  is  to  con- 
nect together  in  series  coils  which  lie  in  fields  of  like  polarity, 
it  is  evident  that  opposite  segments  are  connected  together 
only  in  the  case  of  a  four-pole  field,  for  which  this  form  of 
winding  is  generally  used. 

In  general,   for  any  number  of  poles,  the  segments  con- 

nected  together  are  apart,  p  being  the  number  of  pairs 

P 
of  poles,  as  before.     Two  segments  for  each   coil   may  be 


APPLIED   ELECTRICITY.  1981 

used,  but  if  this  scheme  of  winding  is  laid  out  for  a  field 
with  6  poles,  it  will  be  seen  that  the  distribution  of  poten- 
tials around  the  commutator  is  irregular.     By  introducing 

•       360° 
a  third  commutator  segment  for  each  coil  at  a  pomt  — —  = 

120°  removed  from  each  of  the  other  two,  the  distribution 
of  potentials  will  become  uniform.  In  general,  then,  the 
number  of  segments  in  the  commutator  for  this  form  of 
winding  will  be  equal  to/  times  the  number  of  coils. 

31 35.  There  are  several  forms  of  two-circuit  ring  wind- 
ings besides  the  two  given,  but  as  they  introduce  new  com- 
plications in  the  way  of  cross-connections,  they  are  of 
limited  practical  application.  Of  the  two  given,  the  latter 
is  very  generally  used,  since  it  is  very  simple  and  the  cross- 
connections  are  very  regular.  By  making  the  cross- 
connections  a  part  of  the  commutator  construction,  as  is 
generally  the  practice,  the  winding  itself  is  as  simple  as  a 
plain  ring  winding. 

The  fact  that  there  are  twice  as  many  commutator  seg- 
ments as  coils  is  also  advantageous  in  reducing  the  differ- 
ence of  potential  between  segments.      (See  Art.  3114.) 

3136.  In  a  two-circuit  ring  winding,  a  greater  E.  M.  F. 

will  be  generated  than  in  a  multiple-circuit  winding  with 

the  same  number  of  conductors,    since  in  the   two-circuit 

winding  the   number  of  conductors  connected   in  series  is 

c 
always  — ,  while  in  the  multiple-circuit  winding  it  is  always 

— .  The  E.  M.  F.  of  the  two-circuit  winding  is  then  p 
2/  b  r 

times  as  great  as  that  of  the  multiple-circuit  winding  with 
the  same  number  of  conductors,  and  by  introducing  this 
term  in  formula  480,  given  in  Art.  3104,  it  becomes 

^  =  1^-  (482.) 

which  is  the  formula  for  determining  the  E.  M.  F.  of  any 
two-cirmit  winding. 


1982  APPLIED   ELECTRICITY. 

BIPOLAR    DRUM    WITVDIIVGS. 

3137,  From  the  nature  of  the  drum  winding,  each  coil 
must  have  at  least  two  active  conductors,  in  order  to  bring 
both  ends  of  the  coil  to  the  front  of  the  armature  core; 
further,  these  two  conductors  must  lie  in  fields  of  opposite 
polarity,  and  the  E.  M.  F.'s  generated  in  the  two  conductors 
must  be  as  nearly  as  possible  in  phase,  in  order  that  they 
may  add  together  without  opposition.  From  an  examina- 
tion of  the  drum  winding  shown  in  Fig.  1160,  it  will  be  seen 
that  the  winding  is  constructed  as  follows:  The  surface  of 
the  armature  core  being  divided  into  a  number  of  zvinding 
spaces  equal  to  tzvice  the  number  of  coils  the  winding  is  to 
have,  then,  starting  at,  for  example,  segment  da,  coil  A  A 
is  formed  by  carrying  the  conductor  along  one  of  the  wind- 
ing spaces  to  the  back  of  the  core,  across  the  back  to  the 
winding  space  alongside  the  one  diametrically  opposite  the 
one  in  which  the  coil  was  begun,  then  along  this  winding 
space  to  the  front  and  up  to  commutator  segment  a  c,  the 
one  next  on  the  right  of  segment  d  a.  From  this  point 
the  next  coil  {C  C)  is  started,  the  conductor  being  carried 
along  the  core  from  front  to  back,  not  in  the  winding  space 
next  to  that  occupied  by  the  conductor  first  considered,  but 
in  the  second  winding  space  to  the  right  of  that  one ;  the 
one  skipped  over  will  be  filled  by  another  coil.  The  coil  is 
completed  in  the  same  manner  as  the  first,  the  end  be- 
ing carried  to  the  next  segment  to  the  right  of  a  c.  By 
proceeding  with  the  remainder  of  the  coils  in  the  same 
manner,  it  will  be  seen  that  when  half  the  coils  (^4  A, 
C  C,  B'  B\  and  D'  D')  are  wound  on  the  core,  there  is 
an  even  spacing  of  conductors  all  around,  but  only  half  the 
commutator  segments  are  utilized,  and  only  alternate  wind- 
ing spaces  occupied.  To  proceed  with  the  winding,  coil 
A'  A'  is  wound,  starting  at  segment  a'  d'  and  carrying  the 
conductor  along  the  core  from  front  to  back  in  the  winding 
space  between  spaces  occupied  by  the  parts  of  coils  A  A 
and  C  C  that  return  from  back  to  front,  then  across  the 
back  and  along  the  core  from  back  to  front  in  the  winding 
space  left  between  the  first  parts  of  coils  A  A  and  D  D  that 


APPLIED   ELECTRICITY.  1983 

were  wound,  and  then  to  segment  a'  c' .  The  remainder  of 
the  coils,  C  C\  B  B,  and  D  D,  are  wound  on  in  a  similar 
manner,  and  the  end  of  coil  D  D  connects  with  segment 
da  from  which  the  winding  started,  thus  forming  a  closed- 
coil  winding. 

3138.  If  it  were  desirable  to  make  each  coil  of  more 
than  two  turns,  the  extra  turns  would  be  wound  around  the 
core  in  the  same  winding  spaces  occupied  by  the  first  two 
before  carrying  the  lead  to  the  commutator  segment  and 
proceeding  with  the  next  coil.  In  practice,  this  is  generally 
done,  the  size  of  the  coils  being  so  calculated  that  the  whole 
of  the  armature  surface  is  covered.  In  the  diagrams  used 
to  represent  the  various  drum  windings,  to  prevent  con- 
fusion, only  a  few  coils,  with  two  conductors  per  coil,  will  be 
represented. 

3139.  In  drum  windings  there  are  two  different  factors 
which  correspond  to  the  pitch  as  used  in  two-circuit  ring 
windings,  namely,  the  number  of  winding  spaces  skipped 
over  in  connecting  together  the  oppositely  situated  con- 
ductors of  the  sajne  coil,  across  the  back  (arid  also  across  the 
front,  if  each  coil  has  more  than  two  conductors),  which  is 
called  the  back  pitch,  and  the  number  of  winding  spaces 
skipped  over  in  connecting  together  succeeding  coils,  across 
the  front  of  the  core,  which  is  called  the  front  pitch.  In 
the  diagram  given  in  Fig.  1160,  the  back  pitch  is  7  and  the 
front  pitch  5.  In  the  case  of  the  two-circuit  ring  windings 
the  pitch  was  always  taken  in  the  same  direction,  i.  e.,  if  a 
coil  was  connected  to  a  coil  situated  y  coils  to  the  rigJit^  this 
latter  was  in  turn  connected  to  a  coil  y  coils  to  the  right 
again.  In  the  drum  winding  given  in  Fig.  1160,  however, 
the  front  pitch  is  in  the  opposite  direction  to  the  back 
pitch,  and  this  is  indicated  by  giving  the  front  pitch  a 
—  sign.      Thus,  the  back  pitch  being  7,  the  front  pitch  is  —5. 

31 40.  The  method  of  representing  drum  windings 
used  in  Fig.  1160  is  not  convenient,  since  it  is  difficult  to 
represent  the  connections  across  the  back  of  the  core  with- 
out a  confusion   of  lines.      Fig.  1168  shows  the  method  of 


1984  APPLIED   ELECTRICITY. 

diagrammatically  representing  drum  windings  that  will  be 
used  in  this  discussion.  This  winding  is  the  same  as  that 
represented  in  Fig.  1160,  it  being  imagined  that  the  arma- 
ture and  winding  is  expanded  from  the  back  until  it  becomes 
a  flat  disk.  The  heavy  radial  lines  represent  the  conduct- 
ors on  the  face  of  the  core,  the  lighter  lines  represent  the 
connections  between  them;  the  ring  represents  the  cylindri- 


FiG.  1168. 

cal  surface  of  the  core,  and  the  shaded  parts  represent  the 
portions  of  the  core  that  are  covered  by  the  pole-pieces; 
that  is,  they  represent  the  magnetic  fields.  The  commuta- 
tor and  brushes  are  represented  in  a  similar  manner  as  for 
the  ring  windings. 

3141.     It  will  be  seen  from  this  diagram  (in  which  the 
16  conductors  are  evenly  distributed  on   the  surface  of  the 


APPLIED   ELECTRICITY.  1985 

armature)  that  the  conductors  of  each  of  the  short-circuited 
coils  1-8  and  9-16  do  not  He  in  the  same  part  of  each  neu- 
tral space,  because  they  are  not  diametrically  opposite  on 
the  core. 

With  an  even  number  of  coils,  and  with  the  conductors 
placed  in  one  layer  on  the  surface  of  the  core,  opposite  con- 
ductors can  not  be  connected  together  and  give  a  symmetri- 


FlG.  1169. 

cal  winding.  With  an  odd  number  of  coils,  however,  oppo- 
site conductors  may  be  connected  together,  as  illustrated  in 
Fig.  1169,  which  shows  a  winding  with  9  coils,  i.  e.,  18  con- 
ductors. In  this  winding  the  back  pitch  is  9  and  the  front 
—  7.  In  the  position  shown,  the  coil  formed  of  conductors 
1  and  10,  which  lie  directly  in  the  center  of  the  neutral 
spaces,  is  short-circuited  by  the  +brush.     There  being  an 


1986  APPLIED   ELECTRICITY. 

odd  number  of  commutator  segments,  only  one  coil  is  short- 
circuited  at  a  time, 

3142.  If,  in  the  winding  illustrated  in  Fig.  1168,  alter- 
nate conductors,  e.  g,,  those  with  odd  numbers,  are  moved 
around  to  the  left  until  they  coincide  in  position  with  the 
even  numbered  conductors,  then  the  two  conductors  in  each 
coil  would  be  directly  opposite  each  other,  as  in  the  case  of 
the  winding  with  the  odd  number  of  coils.  With  this  form 
of  winding,  half  of  each  coil  is  in  the  outside  and  half  in 
the  inside  layer  of  windings,  which  introduces  no  difficulty 
in  winding  if  each  coil  consists  of  but  one  turn;  but  if  each 
coil  consists  of  two  or  more  turns,  then  the  fact  that  the 
conductors  of  the  coil  that  are  in  the  inner  layer  must  all 
be  wound  on  before  the  outer  layer  can  be  wound  causes 
serious  difficulties  in  the  winding..  It  is  usually  better  to 
wind  the  coils  side  by  side,  as  represented. 

When  the  coils  are  wound  in  slots  cut  in  the  periphery 
of  the  armature  core  instead  of  being  wound  continuously 
over  the  surface,  it  becomes  an  easy  matter  to  construct 
coils  of  many  turns  of  wire.  These  coils  are  wound  on  a 
form  and  taped,  after  which  they  may  be  slipped  into  place 
and  connected  up. 

3143.  The  possible  variations  in  the  method  of  wind- 
ing bipolar  drum  armatures  are  many.  In  general,  the 
number  of  conductors  must  always  be  even,  although  the 
number  of  coils  may  be  either  odd  or  even.  The  back 
pitch  determines  the  relative  position  on  the  core  of  the 
members  of  a  coil,  from  which  it  follows  that  in  order 
to  have  both  members  in  the  neutral  spaces  at  the  same 
time  the  back  pitch  should  be  very  nearly  equal  (in  bipolar 

iv 
fields)  to  — ,  IV  being  the  number  of  winding  spaces. 

w 
The  back  pitch  obviously  can  not  be  exactly  equal  to—, 

unless  s  (the  number  of  coils)  is  odd.     With  an  even  num- 
ber of  coils  the  nearest  approach  to  this  value  is  evidently 

"ii"  ±  1;  if  +1  is  used,  the  end  connections  are  longer  and 


APPLIED   ELECTRICITY.  1987 

make  more  crossings,  and  the  winding  has  no  particular 
advantage  over  that  resulting  from  the  use  of  —1  in  the 
above  formula.    It  is  better,  then,  to  make  the  back  pitch  = 

^-1. 

2 

3144.  The  front  pitch  determines  the  position  of  a 
coil  relative  to  the  coils  with  which  it  is  immediately  con- 
nected, and  should,  therefore,  differ  from  the  back  pitch 
by  2.  (See  Art.  3137.)  If  the  front  pitch  is  less  than 
the  back  pitch,  each  of  the  coils,  taken  in  the  order  in  which 
they  are  connected,  lies  to  one  side  of  the  coil  preceding  it 
in  the  same  direction  as  the  back  pitch;  for  example,  in 
Figs.  1168  and  1169  the  direction  of  the  back  pitch  is  to 
the  right,  and  the  front  pitch  being  in  each  case  less  than 
the  back  pitch  the  successive  coils  each  lie  to  the  right  of 
that  preceding  it,  e.  g.,  coil  3-12  lies  to  the  right  of  coil 
1-10  (Fig.  1169).  This  is  called  the  advance  of  the 
winding. 

3145.  If  the  front  pitch  is  greater  than  the  back  pitch, 

the  advance    is   opposite    in   direction    to    the    back    pitch. 

There  is  no  particular  advantage  in  this,   however,  and  it 

has  the  disadvantage  that  the  connections  across  the  ends 

of  the  core  are  longer  for  the  same  winding  than  in  the  case 

where  the  back  pitch  and  the  advance  are  both  in  the  same 

direction,  thus  requiring  a  greater  length  of  wire  for  the 

winding  and  increasing  the  number  of  crossings  of  the  end 

connections.      It  is  better,  then,  to  make  the  front  pitch  less 

zv 
than  the  back  pitch,  in  which  case  its  value  would  be  =  — - 

2 

ZV 

—  3,  when  the  back  pitch  =  — 1,  as  noted  above. 

3146.  It  is  possible  to  use  values  for  the  back  and  the 
front  pitch  which  are  less  than  those  given  by  the  above 
formulas,  as  indicated  in  Fig.  1170,  which  gives  a  winding 
in  which  i'=  10  and  w  =  20;  the  back  pitch  =  +7  and  the 
front  pitch  =  —  5. 

In  the  position  represented  injthis  figure  the  coil  formed 


1988  APPLIED  ELECTRICITY. 

of  conductors  1  and  8  is  short-circuited  by  the  -fbrush,  and 
that  formed  of  conductors  18  and  11  is  short-circuited  by 
the  —brush.  It  will  be  seen  that  these  coils  do  not  lie 
alongside  one  another,  as  has  been  the  case  in  all  the  pre- 
vious windings  where  s  is  even,  but  instead  are  separated  by 


Fig.  1170. 
conductors  in  which  the  armature  current  is  flowing.      This 
results  in  causing  the  short-circuited  coils  to  lie  on  the  edge 
of,  or  even  in,  the  magnetic  field,  unless  the  width  of  the 
field  is  made  smaller  than  has  been  represented. 

3147.     This  form  of  winding,  where  the  back  pitch  is /^rj-i- 

than 1,  is  called  a  chord  ^s^inding,  and  the  disadvantage 

of  having  the  short-circuited  coils  slightly  out  of  the  neutral 
space  (which  with  a  greater  number  of  coils  would  be  much 


APPLIED   ELECTRICITY. 


1989 


less  than  with  the  few  coils  represented  in  the  diagram)  is  to 
some  extent  balanced  by  the  shorter  length  of  wire  required 
for  the  end  connections  and  the  fewer  crossings  made  by 
them,  providing  the  space  between  the  two  winding  spaces 
occupied  by  a  coil  is  not  less  than  the  width  of  the  field. 

In  addition,  it  will  be  seen  that  where  the  "brushes  are 
shifted  the  current  in  some  of  the  armature  conductors  in- 
cluded in  twice  the  angle  of  lead  of  the  brushes  is  opposite 
in  direction  to  that  in  the  others,  which  reduces  the  counter 
magnetomotive  force  of  the  armature  winding. 

"3148.  Another  modification  of  the  drum  winding  con- 
sists in  giving  to  both  the  front  and  the  back  pitches  the  sa^ne 


Fig.  1171. 
direction.      Fig.  1171  represents  a  winding  in  which  s  =  10, 
as  in  Fig.  1170,  w  =  20,  and  the  front  and  the  back  pitches  are 


1990  APPLIED   ELECTRICITY. 

each  equal  to  -|-9.  It  will  be  seen  that  one  effect  of  giving 
both  pitches  the  same  direction  is  to  make  it  possible  to  have 
both  pitches  equal,  which  is  obviously  not  the  case  when 
they  are  given  opposite  directions.  As  in  the  windings  pre- 
viously considered,  the  winding  space  occupied  by  the  first 
half  of  a  coil  must  be  the  second  winding  space  away  from 
that  occupied  by  the  first  half  of  the  preceding  coil.  (See 
Art.  3137.)  Since  both  pitches  are  in  the  same  direction, 
this  condition  makes  it  necessary  that  the  total  number  of 
winding  spaces  be  equal  (in  bipolar  fields)  to  the  sum  of  the 
front  and  back  pitches,  ±3.  If  /  =  the  average  pitch,  i.  e., 
half  the  sum  of  the  front  and  back  pitches,  then  the  number 
of  winding  spaces  which  must  be  used  is  given  by  the  formula 

w  =  2  J  ±  2.  (483.) 

In  Fig.  1171,  J  =  9,  and  w  might  then  have  been  16  or  20. 
If— 2  is  used,  the  advance  of  the  winding  is  in  the  same 
direction  as  the  pitch;  but  if  -\-'%  is  used  the  advance  is  in 
the  opposite  direction. 

This  is  more  advantageous,  since  the  end  connections  are 
a  little  shorter  for  the  same  number  of  conductors;  hence, 
a  less  length  of  wire  is  required  for  the  winding. 

3149.  In  order  that  all  of  an  even  number  of  winding 
spaces  may  be  passed  over  in  connecting  up  this  form  of 
winding,  both  front  and  back  pitch  must  be  odd,  so  that  if 
they  are  equal  the  average  pitch  will  also  be  odd.  If  the 
front  and  the  back  pitches  differ  by  2,  the  average  pitch 
may  be  even. 

For  example,  with  an  average  pitch  of  8,  the  number  of 
winding  spaces  might  be  ?:£/  =  (2  X  8)  ±  2  =  18  or  14;  since 
each  pitch  must  be  odd,  the  back  pitch  might  be  taken  as  +9 
and  the  front  pitch  as  -]-7,  or  vice  versa. 

In  this  style  of  winding,  both  pitches  having  the  same 
direction,  it  will  be  seen  that  when  the  average  pitch  is  even 
the  number  of  coils  is  odd^  but  when  the  average  pitch  is 
odd  the  number  of  coils  is  even.  Further,  when  the  average 
pitch  is  odd,  the  end  connections  on  both  ends  are  of  the 
same  length,  which  is  often  an  advantage  in  manufacture. 


APPLIED   ELECTRICITY.  1991 

END   COIVIVECXIONS  OF   COILS. 

31 50.  Though  it  has  not  thus  far  been  represented, 
the  end  connections  of  the  drum  winding  must  be  made  to 
avoid  the  armature  shaft  in  crossing  the  ends  of  the  core. 
This  is  accomplished  in  a  variety  of  ways<  In  the  ordinary 
forms  of  drum  winding  with  coils  made  up  of  several  turns 
each,  the  end  connections  of  each  coil  are  simply  carried 
across  the  end  of  the  core  and  bent  out  to  one  side  to  avoid 
the  shaft;  as  each  coil  is  wound,  its  end  connections  are  laid 
over  the  end  connections  of  the  coils  previously  wound,  the 
whole  being  so  disposed  as  to  make  as  nearly  as  possible  a 
symmetrical-looking  winding  when  done.  In  this  form  of 
winding,  the  several  coils  may  be  of  quite  different  lengths, 
those  wound  on  last  being  longer  than  those  first  wound. 

Further,  the  end  connections  lap  over  and  cross  each 
other  in  all  directions,  and  special  precautions  must  be 
taken  to'  insulate  carefully  between  coils,  and  in  case  of 
accident  to  one  of  the  coils  first  wound,  the  rest  of  the  coils 
must  be  removed  before  the  injured  coil  can  be  repaired. 

3151.  It  is  apparent,  then,  that  on  account  of  these 
difficulties  some  other  method  of  winding  is  desirable  which 
shall  not  be  open  to  some  or  all  of  the  above  mentioned 
objections.  In  case  each  coil  consists  of  but  one  turn  (two 
conductors),  the  end  connections  may  be  arranged  as  repre- 
sented in  Fig.  1172,  in  which  C  is  the  drum  armature  core; 
a  and  d  are  the  two  conductors  of  an  armature  coil,  and 
c  and  d  the  two  conductors  of  the  coil  next  succeeding  coil 
a  d  in  the  winding.  Considering  that  the  view  represents 
the  dack  end  of  the  core  and  that  d  is  the  conductor  from 
which  the  winding  starts,  then  the  winding  is  proceeded 
with  as  follows:  Conductor  <^is  bent  down  at  right  angles  at 
the  end  of  the  core  (see  plan,  Fig.  1172)  and  carried  in  a 
spiral  curve  along  the  end  face  of  the  core  to  a  point  «, 
which  is  on  the  diameter  about  at  right  angles  to  the  plane 
of  the  coil,  and  at  a  sufficient  radial  distance  from  the  axis 
of  the  core  to  clear  the  shaft.  At  this  point  the  conductor 
is  bent  outward  at  right  angles,  carried  along  away  from 


1992 


APPLIED   ELECTRICITY. 


the  core  parallel  to  the  shaft  for  a  short  distance,  as  repre- 
sented at  n  (in  the  plan),  then  bent  at  right  angles  again 
and  carried  in  a  spiral  curve  parallel  to  the  end  face  of  the 
drum  and  bent  over  to  form  conductor  a.     In  forming  the 


next  coil  c  d,  which  is  located  two  winding  spaces  away 
from  coil  a  b  (see  Art.  3137),  a  similar  process  is  gone 
through  with,  the  two  spiral  connectors  being  carried  along 
parallel  with  those  of  the  first  coil  to  be  wound,  as  repre- 
sented. 

3152.  It  will  be  seen  that  by  completing  the  whole 
winding  in  a  similar  manner,  the  end  connections  are  situ- 
ated in  two  parallel  planes,  those  in  the  inner  plane  being 
the  connections  from  the  first  conductors  of  the  coils  to  the 
center,  and  those  in  the  outer  plane  being  the  connections 
from  the  center  to  the  last  conductors  of  the  coils.  This 
forms  a  very  symmetrical  winding,  and  the  end  connections 
cross  in  such  a  manner  that  it  is  a  very  simple  matter  to 
insulate  them  thoroughly.  It  is  evident  that  the  number  of 
short  lengths  of  conductors  at  n  (Fig.  1172)  is  equal  to  the 
number  of  coils;  hence,  the  distance  of  «  from  the  axis  must 
be  great  enough  to  allow  this  number  of  conductors  to  lie 
side  by  side,  with  insulation  between.  If  the  conductors  are 
of  uniform  section  throughout,  and  are  spaced  closely  on  the 
surface  of  the  core,  this  might  require  that  the  point  7i  be 


APPLIED   ELECTRICITY.  1993 

too  far  from  the  axis.  To  avoid  tliis  difficulty,  the  end  con- 
nections may  be  made  in  the  form  of  separate  connectors, 
of  thin  sheet  copper,  wide  enough  to  give  the  necessary 
cross-section,  and  bent  to  the  proper  shape ;  these  are  placed 
in  position,  with  the  width  of  the  copper  strip  parallel  to  the 
shaft,  and  fastened  to  the  conductors  on  the  face  of  the  ar- 
mature core.  In  such  a  "built  up"  winding,  the  active 
conductors  are  often  made  of  heavy  copper  bars  of  rectangu- 
lar section,  to  which  the  end  connectors  are  riveted  or 
soldered.     Fig.  1173  shows  one  form  of  end  connector  made 


Fig.  1173. 

from  a  rectangular  piece  of  sheet  copper,  which  is  slotted 
for  almost  its  entire  length.  The  two  tongues  of  metal  thus 
formed  are  bent  over,  one  to  the  right  and  one  to  the  left, 
forming  the  end  connector  represented  in  the  figure.  The 
proper  curves  for  the  spiral  parts  of  the  end  connector  may 
best  be  determined  by  laying  them  out  on  the  drawing-board, 
and  by  trials  determining  which  curve  will  give  the  most  uni- 
form clearance  between  adjacent  connectors.  When  using 
these  end  connectors,  the  shorter  conductors  of  the  winding 
may  as  well  be  under  as  alongside  the  longer  conductors,  if 
their  number  is  properly  chosen,  thus  forming  a  two-layer 
winding. 

3153.  In  case  it  is  desired  to  use  more  than  one  turn 
in  each  coil,  a  winding  which  is  usually  attributed  to  Eicke- 
meyer  may  be  used.  In  this  winding  each  coil  is  wound  on 
a  wooden  form  to  the  proper  shape,  and  the  proper  number 
are  then  placed  in  position  on  the  armature  core.  The  shape 
of  the  coil  as  completed  is  approximately  rectangular,  the 


1994  APPLIED   ELECTRICITY. 

ends  of  the  rectangle  being  bent  in  a  manner  similar  to  the 
end  connections  illustrated  in  Fig.  1172,  so  that  when  the 
coils  are  placed  in  position  on  the  core,  the  end  connections 
of  each  coil  as  a  whole  cross  in  the  same  manner  as  in  the 
winding  described  in  Art.  3151,  where  each  coil  consists 
of  a  single  turn.  Of  the  two  sides  of  the  coil  which  form 
the  active  conductors,  one  is  shorter  than  the  other  by  reason 
of  difference  in  the  planes  in  which  the  two  parts  of  the  end 
connections  lie.  (See  Fig.  1172.)  This  shorter  side,  in  the 
completed  winding,  may  lie  beneath  or  alongside  the  longer 
side  of  the  neighboring  coil,  thus  forming  a  two-layer  or  a 
single-layer  winding,  as  the  designer  may  decide. 

315-4.  By  referring  to  the  various  diagrams  for  drum 
windings  which  have  been  given,  it  will  be  seen  that  in  all 
the  windings  the  adjacent  conductors  which  lie  in  the  neutral 
spaces  have  between  them  nearly  or  quite  the  full  difference 
of  potential  that  exists  between  the  brushes.  This  is  not 
quite  so  marked  in  the  chord  Winding  (Fig.  1170),  which  is 
one  advantage  of  this  form  of  winding. 

In  the  two-layer  winding  it  will  be  seen  that  as  the  two 
adjacent  conductors  are  placed  one  over  the  other,  the  full 
difference  of  potential  exists  between  the  members  of  the 
two  layers  at  such  time  as  they  are  in  the  neutral  spaces. 
This  feature  requires  that  the  adjacent  conductors  in  single- 
layer  windings  and  the  two  layers  in  two-layer  windings  be 
carefully  insulated  one  from  the  other. 


MULTIPOLAR    DRUM    TVINDINGS. 

3155.  The  use  of  the  drum  winding  for  large  multi- 
polar armatures  has  become  very  general,  as  it  possesses 
many  advantages.  In  these  larger  machines  the  number  of 
conductors  in  the  winding  may  usually  be  so  chosen  that 
only  one  turn  is  required  for  each  coil,  and  each  coil  is  made 
up  of  two  active  conductors  made  from  copper  bars  and  two 
separately  formed  end  connectors. 

For  greater  rnechanical  security,  these  bars  are  let  into 


APPLI£.D   ELECTRICITY.  1995 

grooves  cut  or  punched  in  the  periphery  of  the  core,  which 
grooves  are  necessarily  (as  will  be  pointed  out  later)  narrow, 
close  together,  and  comparatively  deep.  Such  a  winding  as 
this  is  known  as  a  bar  winding,  and  if  the  grooves  or  slots 
in  the  armature  core  have  overhanging  tops,  so  that  the 
conductors  are  thoroughly  enclosed,  the  armature  is  said  to 
be  iron-clad. 

3156.  One  of  the  principal  features  of  a  drum  winding 
is  that  opposite  sides  of  a  coil  must  be  in  magnetic  fields  of 
opposite  polarity.  It  follows  that  a  drum  winding  that  is 
designed  for  a  two-pole  field  will  not  give  any  E.  M.  F.  if 
rotated  in  a  four-pole  field,  since  opposite  sides  of  a  coil 
would  then  be  in  fields  of  like  polarity. 

In  order  to  obtain  a  drum  winding  for  a  multipolar  ma- 
chine, it  is  necessary  then  that  conductors  which  are  similarly 
situated  with  respect  to  fields  of  opposite  polarity  should  be 
connected  together  to  form  the  armature  coils.  To  accom- 
plish this,  the  pitch  of  the  winding  must  be  something  near 

the   value  given   by  —— ,  zv  being  the  number  of  winding 

spaces  2:^A  p  the  number  of  pairs  of  poles,  as  before. 

As  in  the  bipolar  windings,  the  front  pitch  should  equal 
the  back  pitch  ±  3  when  the  two  pitches  are  in  opposite 
directions,  and  as  the  total  number  of  winding  spaces  must 
be  even,  both  pitches  must  be  odd  in  order  that  all  the  wind- 
ing spaces  may  be  passed  through. 


LOOP   A^^IIVDING. 

3157.  When  the  front  and  the  back  pitches  are  of  oppo- 
site sign,  halftYiQ  conductors  under  any  pair  of  adjacent  poles 
are  connected  together  in  series,  and,  therefore,  form  one 
circuit  of  the  armature.  This  results  in  there  being  as  many 
armature  circuits  as  poles,  as  in  the  simple  multipolar  ring, 
with  the  same  necessity  for  either  as  many  brushes  as  poles 
or  a  cross-connected  commutator  and  a  single  pair  of  brushes. 

This  type  of  multipolar  drum  winding  is  called  a  loop 
^fvinding,  since,  in  following  the  course  of  the  winding,  a 


1996  APPLIED  ELECTRICITY. 

series  of  loops  is  formed,  caused  by  the  opposite  sign  of  the 
two  pitches. 

3158.  Fig.  1174  is  a  diagram  of  a  four-pole  loop  wind- 
ing, in  which  32  conductors  are  represented.  The  back  pitch 
is  taken  as  +9  and  the  front  pitch  as  —7. 

As  in  the  previous  diagrams,  the  conductors  which  make 
up  the  coils  that  are  short-circuited  by  the  brushes  have  no 


Fig.   1174. 

arrows,  the  arrows  near  the  other  conductors  indicating  the 
direction  of  the  E.  M.  F.  induced  in  them. 

This  form  of  winding  needs  no  further  elaboration.  It 
can  be  used  for  6,  8,  or  a  greater  number  of  poles,  and  its 
E.  M.  F.  may  be  calculated  in  the  same  manner  as  for  the 
multipolar  ring  winding  with  as  many  armature  circuits  as 
poles.     (Art.  3126.) 


APPLIED    ELECTRICITY.  1997 

When  this  foim  of  winding  is  used  in  slotted  armatures 
(see  Art.  3155),  the  only  requirement  that  has  not  already 
been  given  is  that  the  total  number  of  conductors  must 
be  some  even  number,  and  the  total  number  of  conductors 
must  be  a  multiple  of  the  number  of  slots. 


3159.  In  bipolar  drum  windings,  giving  both  pitches 
the  same  direction  has  little  effect  on  the  resulting  wind- 
ing; in  multipolar  drum  windings,  the  efifect  is  marked.  If 
both  pitches  have  the  same  direction,  the  winding,  passing 
from  front  to  back  under  one  pole-piece  and  returning  to 
the  front  again  under  the  next  pole-piece,  would  continue 
by  passing  from  front  to  back  under  the  next  pole-piece, 
progressing  in  the  same  direction  as  before,  and  thus  form- 
ing a  series  of  waves,  instead  of  loops,  as  when  the  pitches" 
have  opposite  directions.  (Art.  3157.)  This  style  of 
winding  is  then  called  a  wave  >viiid[ing. 

As  in  the  bipolar  winding,  the  pitch  may  be  the  same, 
both  front  and  back,  in  which  case  it  must  be  odd,  or  the 
front  and  the  back  pitch  may  differ  by  2,  in  which  case  they 
must  both  be  odd,  making  the  average  pitch  even. 

31 60.  It  has  been  pointed  out  that  the  wave  winding 
advances  in  a  series  of  waves  or  steps,  and  it  is  evident  that, 
after  making  a  number  of  steps  equal  to  the  number  of 
poles,  the  winding  must  come  to  the  second  winding  space 
from  that  containing  the  conductor  with  which  the  wind- 
ing started.  From  this  it  follows  that  the  total  number 
of  winding  spaces  possible  with  this  form  of  winding  is 
equal  to  the  product  of  the  number  of  poles  and  the  average 
pitch,  ±  2,  or,  as  expressed  in  the  symbols  previously  used, 

^v  =  %py  ±^.  (484.) 

It  will  be  noted  that  this  is  the  same  formula  as  that  used 
for  the  bipolar  drum  winding,  in  which  both  pitches  were 
given  the  same  direction  (formula  483),  with  the  addition 
of  the  term/.     (See  Art.  3148  and  Fig.  1171.) 


1998 


APPLIED   ELECTRICITY. 


3161.  Fig.  1175  is  a  diagram  of  a  four-pole  wave  wind- 
ing, in  which  y  =  9.  Therefore,  w  =  2/ j  ±  2  =  34  or  38. 
The  former  number  (34)  is  used  in  this  diagram. 

It  will  be  seen  from  this  diagram  that  the  wave  winding 
results  in  a  two-circuit  winding,  requiring  only  two  brushes, 


Fig.  1175. 


This  holds   true 


just  as  the  two-circuit  multipolar  rings, 
whatever  the  number  of  poles  of  the  field. 

The  advance  of  this  winding  is  in  the  same  direction  as 
the  pitch.  If  +2  had  been  used  in  the  formula,  38  conduct- 
ors would  have  been  required,  and  the  advance  would  have 
been  opposite  in  direction  to  the  pitch. 

If  the  average  pitch  had  been  taken  as  8,  using +9  for 
the    back  and  +7  for  the  front  pitch  (or  vice  versa),    the 


APPLIED   ELECTRICITY.  1999 

same  number  of  conductors  might  have  been  used;  i.e., 
w  =  2/j/  ±  2  =  (2  X  2  X  8)  ±  3  =  30  or  34. 

For  bar-wound  armatures,  it  is  better  to  use  +3  in  the 
formula,  and  the  same  pitch  on  both  ends,  if  the  number  of 
conductors  required  will  allow,  since  that  will  give  the  most 
economical  system  of  end  connections. 

From  Fig.  1175  it  will  be  seen  that  each  brush  alternately 
short-circuits  two  coils  that  are  in  series,  and  the  point 
where  these  two  coils  are  connected  is  the  commutator  seg- 
ment that  is  as  nearly  as  possible  opposite  the  brush  that  is 
short-circuiting  the  coils. 

3162.  Sometimes  it  is  desired  to  use  a  two-circuit 
armature,  but  the  ordinary  form  would  give  too  great  a  dif- 
ference of  potential  between  segments.  Since  in  this  form 
of  winding  there  are/  coils  included  between  every  adjacent 
pair  of  commutator  segments,  an  additional  commutator 
segment  may  be  inserted,  in  such  a  case,  between  each  pair 
of  segments  of  the  winding  as  already  given,  each  of  these 
interpolated  segments  being  connected  with  the  segment  of 
the  original  commutator  that  is  directly  opposite  it.  This  is 
illustrated  in  Fig.  1176,  which  shows  a  four-pole  wave  wind- 
ing with  30  conductors,  in  which  the  pitch  (both  front  and 
back)  is  -[-7.  A  number  of  commutator  segments  equal  to 
the  number  of  conductors  (30)  is  used ;  alternate  segments 
are  connected  to  the  winding,  and  each  of  the  rest  is  con- 
nected to  the  segment  directly  opposite,  which  is  one  of 
those  connected  directly  to  the  winding.  The  result  of  this 
interpolated  segment  construction  is  that,  unless  the  brushes 
are  wider  than  one  segment,  only  one  coil,  consisting  of  two 
conductors,  is  short-circuited  at  a  time,  and  the  difference 
of  potential  between  adjacent  segments  is  only  that  gen- 
erated in  one  coil,  instead  of  that  generated  in/  (2)  coils,  as 
would  be  the  case  if  the  interpolated  segments  were  not 
used. 

31 63.  When  in  the  position  shown  in  the  figure,  the  coil 
formed  of  conductors  1  and  8  is  short-circuited  by  the 
—  brush.     If  the  armature  is  rotated  in  the  direction  indicated 


2000  APPLIED   ELECTRICITY. 

by  the  arrow,  the  next  coil  to  be  short-circuited  is  that 
formed  of  conductors  9  and  16,  by  the  4-brush;  the  next  is 
the  coil  formed  by  conductors  ^^  and  17,  by  the  —brush; 


Fig.  1176. 

and  so   on,    as  the  armature  rotates.     (Compare  this  with 
Art.  3132.) 

Only  two  of  the  cross-connectors  carry  the  current  at  any 
one  time,  as  indicated  by  the  arrow,  Fig.  1176. 

3164.     With  more  than  two  pairs  of  poles,  an  additional 
set  of  interpolated  segments  must  be  used  for  each  pair  of  poles 

increase  over  two,  and  these  must  be  located ^  apart  on 

the  commutator,  and  connected  together.     This  makes  such 


APPLIED    ELECTRICITY.  2001 

a  complicated  system  of  connections  that  the  interpolated 
segment  construction  is  seldom  used  for  fields  with  more  than 
four  poles,  although,  when  the  number  of  pairs  of  poles  (/) 
is  even,  one  set  of  interpolated  segments  connected  to  the 
segments  directly  opposite  may  be  used,  thus  halving  the 
difference  of  potential  between  segments  and  the  number  of 
conductors  short-circuited  at  a  time.  Hence,  with  an  eight- 
pole  field,  one  set  of  interpolated  segments  would  reduce 
the  difference  of  potential  between  adjacent  segments  to  the 
E.  M.  F.  generated  in  two  coils. 

3165.  From  the  formula  for  the  number  of  winding 
spaces  in  the  wave  winding,  zu  =  '^p y  ±  3,  it  will  be  seen 
that  w  is  always  twice  an  odd  number  when/"  is  even,  as  in 
4,  8,  or  12  pole  machines;  while  w  may  be  twice  either  an 
odd  or  an  even  number  when/  is  odd,  as  in  2,  6,  or  10  pole 
machines.  From  this  it  follows  that  with  bar-wound  arma- 
tures arranged  for  two-circuit  single  winding,  w  must  be 
such  a  number  that  the  number  of  conductors  per  slot  and 
2/,  the  number  of  poles,  cannot  have  a  commor^^  factor 
greater  than  2.  For  example,  four  conductors  per  slot  can 
not  be  used  in  an  8-pole  machine,  as  4  and  8  have  a  common 
factor  greater  than  2.  Four  conductors  per  slot  can,  how- 
ever, be  used  with  six  poles.  It  would  seldom  be  the  case 
that  a  greater  number  of  conductors  per  slot  than  four 
would  be  desired,  owing  to  mechanical  difficulties  in  con- 
structing the  winding. 

Unless  an  interpolated  segment  commutator  is  used,  the 

w 
number  of  commutator  segments   is  equal  to  -— ,  hence  is 

2 

odd  when/  is  even,  and  may  be  either  even  or  odd  when/ 
is  odd. 

3166.  In  multipolar  drum  armatures,  end  connec- 
tions similar  to  those  described  in  Art.  3152  are  almost 
invariably  used,  especially  as  almost  all  the  larger  sizes  of 
drum-wound  armatures  employ  bars  for  the  active  con- 
ductors and  flat  strip  end  connectors,  the  armature  coils 
then  consisting  of  but  two  active  conductors  each. 


2002  APPLIED   ELECTRICITY. 

In  case  it  is  desirable  to  use  more  than  two  active  con- 
ductors per  coil,  the  type  of  winding  described  in  Art.  31 53, 
in  which  the  coils  are  wound  to  shape  on  a  separate  form 
and  afterwards  placed  in  position  on  the  core,  may  be  very 
advantageously  used,  especially  with  slotted  armatures. 


MULTIPLE    WIIVDINGS. 

316T.  Sometimes  in  large  machines  for  large  current 
output  the  size  of  the  conductors  required  and  the  volume 
of  current  that  must  be  commuted  at  the  brushes  are  both 
inconveniently  large  with  the  ordinary  forms  of  winding,  as 
already  described.  To  avoid  these  difficulties,  two  or  more 
separate  windings  on  the  same  armature  may  be  employed, 
each  of  which  will  then  furnish  its  share  of  the  required 
current.  A  separate  commutator  may  be  employed  for  each 
winding,  in  which  case  the  corresponding  brushes  of  each 
commutator  must  be  connected  in  parallel;  but  as  this  leads 
to  undesirable  complications,  it  is  much  better  to  combine 
the  various  commutators  into  one,  by  inserting  the  succes- 
sive segments  of  one  commutator  between  the  similar  seg- 
ments of  the  other.  The  various  windings  are  then  con- 
nected in  parallel  by  using  a  wide  brush,  which  must 
evidently  be  of  sufficient  span  to  be  always  in  contact  with 
at  least  one  segment  that  is  connected  to  each  winding,  so 
that  if  there  are  in  separate  windings,  each  brush  must  have 
a  span  not  less  than  that  of  in  segments.  Under  these 
conditions,  the  coils  of  the  successive  windings  will  be  short- 
circuited  one  at   a  time,  and  the  volume  of  current  commu- 

tated  will  be  only  —  of  that  which  would  be  short-circuited 
in 

if  a  similar  form  of  single  winding  were  employed  for  the 

same  current  output. 

Such  a  winding  as  has  been  described  is  known  as  a  mul- 
tiple ^winding,  to  distinguish  it  from  those  forms  in  which 
the  conductors  are  so  connected  as  to  form  a  single  closed- 
coil  winding. 

Any    specific    winding    is  usually  spoken  of   as  a  double, 


APPLIED   ELECTRICITY.  3003 

triple^  etc.,  winding,  according  to  the  number  of  separate 
windings  employed. 

3168.  If  a  given  number  of  conductors  which,  when 
connected  up  into  any  particular  form  of  single  closed-coil 
winding,  will  give  an  E.  M.  F.  of  V  volts,  are  so  connected 
as  to  give  in  separate  windings  of  the  same  form,  all  con- 
nected in  parallel,  there  will  be  but  —  as  many  of  the  con- 
ductors connected  in  series  as  in  the  single  winding,  hence 

V 
the  E.  M.  F.  will  be  only  —  volts.     To  apply  the  formulas 

given  for  finding  the  E.  M.  F.  developed  in  a  winding  con- 
sisting of  a  certain  number  of  conductors  (formulas  480 
and  482),  it  is  only  necessary  then  to  introduce  the  term 
;;/  (the  number  of  separate  windings)  into  the  denominator 
of  the  formula,  so  that  for  multiple-wound  iniiltiple-cimiit 
windings  the  formula  becomes 

and    for   multiple-wound    two-circuit  windings  it   becomes 


p_     cpNS 


3169.  The  principle  of  multiple  winding  may  be  ap- 
plied to  any  form  of  closed-coil  winding,  if  desired,  and, 
further,  by  properly  selecting  the  number  of  coils  and  their 
order  of  succession,  the  end  of  one  winding  may  be  joined 
to  the  beginning  of  the  next,  and  so  on,  thus  forming  a 
single  reentrant  system  of  the  whole  series  of  conductors. 
This  may  also  be  modified,  as  will  be  pointed  out,  to  make 
the  windings  form  a  number  of  separate  reentrant  systems 
which  will  be  some  whole  factor  of  ;;/.  That  is  to  say,  the 
conductors  of  a  multiple-wound  armature  having  vi  wind- 
ings may  be  combined  as  m  separate  reentrant  sj'stems, 
1  reentrant  system,  or  a  number  of  separate  reentrant  sys- 
tems equal  to  some  whole  factor  of  m.     In  practice,  it  is 


2004  APPLIED   ELECTRICITY. 

seldom  that  in  exceeds  3  or  4,  although  it  may  be  any  whole 
number  within  reasonable  limits. 

The  application  of  the  principle  of  multiple  windings 
to  the  various  types  of  armature  windings  will  now  be 
taken  up. 

MULTIPLE-WOUND    MULTIPLE-CIRCUIT  RING    "WINDINGS. 

31 70.  The  multiple-circuit  winding  is  the  simplest 
form  of  ring  winding,  and,  as  has  already  been  pointed 
out,  it  may  be  used  in  fields  having  any  number  of  pairs  of 
poles  without  changing  the  connections. 

Since  the  adjacent  coils  of  a  single-wound  ring  are  con- 
nected together,  and    for    multiple  windings   the    separate 


Fig.  1177. 

coils  of  each  winding  are  supposed  to  lie  between  successive 
coils  of  the  others,  it  follows  that,  in  connecting  up  the  coils 
of  a  ring  winding  to  form  vi  separate  windings,  each  coil  is 
connected  to  the  inth.  coil  on  each  side ;  that  is,  in  —  1  coils 
are  skipped  over  in  connecting  successive  coils  of  the  wind- 


APPLIED   ELECTRICITY. 


3005 


ing.  This  is  shown  in  Fig.  1177,  which  represents  a  two-pole 
multiple-wound  multiple-circuit  ring  armature  of  36  coils, 
in  which  7/i  =  2.  Consequently,  in  connecting  successive 
coils,  2  —  1  =  1  coil  is  skipped  once,  and  alternate  coils  are 
connected  in  each  winding.  Coils  numbered  i,  2,  S,  etc., 
represent  the  one  winding,  and  coils  1\  2\S\  etc.,  represent 
the  other. 

3171.  It  will  be  seen  that,  in  connecting  alternate  coils 
of  the  even  number  (36)  which  is  used  in  this  case,  the  end 
of  the  18th  coil  is  connected  to  the  first  coil,  thus  forming 
one  reentrant  system,  so  that  a  fresh  start  must  be  made 
to  form  the  second  winding,  which,  therefore,  forms  a  second 
reentrant  system. 


Fig.  1178. 

This  results  from  the  fact  that  the  total  number  of  coils 
is  divisible  by  the  number  of  windings,  without  a  remainder. 

If  the  number  of  coils  is  so  chosen  that  there  is  a  remain- 
der, then,  after  passing  through  alternate  coils  once  around 
the  armature,  the  end  of  the  last  coil  connected  will  not  con- 


2006  Applied  electricity. 

nect  with  the  beginning  of  the  coil  from  which  the  winding 
was  started,  but  with  one  on  one  side  or  the  other  of  it, 
thus  starting  the  second  winding,  which  ends  at  the  begin- 
ning of  the  first  coil  of  the  first  winding;  the  two  windings 
thus  form  a  single  reentrant  system. 

This  is  illustrated  in  Fig.  1178,  which  represents  a  two-pole 
multiple-circuit  multiple-wound  armature  having  33  coils,  in 
which  111  =  2,  as  before.  The  coils  are  numbered  from  1  to 
33,  inclusive,  in  the  order  in  which  they  are  connected.  It 
will  be  seen  that,  after  passing  through  alternate  coils  once 
around  the  armature,  thus  passing  through  17  coils,  the 
next  coil  in  succession  is  coil  18,  immediately  to  the  right  of 
coil  1,  which  is  then  the  beginning  of  the  second  winding, 
which  ends  with  coil  1. 

3172.  To  make  a  single  reentrant  winding,  when  in  = 
2,  the  number  of  coils  must  be  odd.  This  being  the  case, 
the  number  of  commutator  segments  is  odd,  and  but  one 
coil  is  short-circuited  at  a  time,  unless  the  brush  has  a  span 
greater  than  that  of  two  segments.  In  the  case  illustrated 
in  Fig.  1178,  coil  26  is  short-circuited  by  the— brush;  a 
moment  later,  the  -{-brush  will  short-circuit  coil  18,  then 
the —brush  will  short-circuit  coil  10,  then  the -{-brush  coil 
2,  and  so  on. 

3173.  In  general,  for  this  class  of  windings  (which,  as 
already  stated,  may  be  applied  to  fields  having  any  reason- 
able number  of  pairs  of  poles),  if  the  number  of  coils,  s,  is  a 
multiple  of  the  number  of  windings,  ;//,  the  conductors  will 
connect  together  into  in  separate  reentrant  systems  ;  while, 
if  the  number  of  coils  is  mutually  prime  with  vi,  the  con- 
ductors will  join  together  into  a  single  reentrant  system. 
For  example,  a  multiple-circuit  multiple-wound  armature 
where  m  =  3  is  to  have  in  the  neighborhood  of  50  coils.  If 
48  or  51  coils  is  the  number  used,  three  separate  reentrant 
systems  will  result,  each  containing  -*3^-  =  16  or  -y-  =  17  coils. 
If  49  or  50  coils  are  used,  a  single  reentrant  system  will  re- 
sult.    When  m  =  4,  or   any  even   number,  the  number  of 


APPLIED   ELECTRICITY.  2007 

reentrant  systems  that  will  result  with  any  given  number 
of  coils,  s,  will  be  equal  to  the  greatest  common  factor  of  m 
and  s.  Thus,  when  ;;/  =  4  with  48  coils,  the  greatest  com- 
mon factor  being  4,  that  number  of  separate  reentrant  sys- 
tems will  result;  with  49  coils,  the  greatest  common  factor 
is  1,  and  one  reentrant  system  will  result.  With  50  coils, 
however,  the  greatest  common  factor  is  2,  so  that  two  sepa- 
rate reentrant  systems  will  result,  each  made  up  of  2  of  the 
4  windings.      (Compare  this  with  Art.  3171.) 


MULXIPLE-IVOUND    T^VO-CIRCUIT    RING    WINDINGS. 

31 74.  The  application  of  the  principle  of  multiple  wind- 
ings to  this  form  of  armature  winding  is  not  materially  dif- 
ferent from  the  cases  just  considered. 

In  the  single  winding,  described  in  Arts.  3129  to  3133, 

the  number  of  coils  in  the  winding  is  found  from  formula 
481,^=/J±1,  the  last  term  (±1)  being  introduced  in 
order  that  the  winding  should  form  a  single  two-circuit 
winding.  To  apply  this  formula  to  multiple-wound  two- 
circuit  windings,  it  is  only  necessary  to  substitute  in,  the 
number  of  separate  windings  desired,  for  1,  which  gives  the 
following  formula  : 

s=py±m.  (487.) 

If  jK  (the  pitch)  is  a  multiple  of  in,  then  s  will  also  be  a 
multiple  of  ?«,  and,  as  in  the  multiple-circuit  windings,  m 
separate  reentrant  systems  will  result  ;  while  if  j  and  m  are 
mutually  prime,  then  s  will  not  be  a  multiple  of  in,  and  a 
single  reentrant  system  will  result.  In  fact,  the  number  of 
separate  reentrant  systems  which  will  result  with  any  given 
number  of  coils  will  be  equal  to  the  greatest  common  factor 
of  in  and  y. 

3175.  For  example,  a  four-pole  two-circuit  ring  wind- 
ing, with  a  pitch  of  11  and  3  windings  (j  =  11,  in  =  3)  could 
have  s  =p y  ±  3  =  22  ±  3  =  25  or  19  coils,  and  11  and  3  be- 
ing mutually  prime,  a  single  reentrant  system  would  result 
with  either  number.     Fig.   1179  represents  the  above  case, 


2008 


APPLIED   ELECTRICITY. 


25  being  the  number  of  coils  used.  It  will  be  seen  that  this 
winding  is  of  the  same  type  as  the  single  winding  illustrated 
in  Fig.  1166.  In  this  case  the  coils  are  numbered  from  1 
to  25;  in  addition,  the  numbers  1',  2\  S',  etc.,  show  the  order 
in  which  the  successive  coils  are  connected.     This  being  a 


Fig.  1179. 


triple  winding,  the  brushes  are  made  of  the  same  span  as 
three  segments;  the +brush  short-circuits  coils  8  and  19, 
and  the  —brush  short-circuits  coils  2  and  13,  the  rest  of  the 
coils  having  arrow-heads  showing  the  direction  of  the  current 
in  them. 

Each  of  the  three  windings  of  this  example  being  a  two- 
circuit  winding,  there  are  six  circuits  through  the  armature. 
On  tracing  these  out,  starting  from  the  —brush,  it  will  be 


APPLIED   ELECTRICITY. 


2009 


found  that  the  various  coils  are  divided  among  the  circuits 

as  follows: 

'    j     1  —  12  —  23  —  9  —  20  )    "^ 

•j  15-    4_18-7  j 

(25  —  11  —  22  I    I  4- 

j  24  -  10  -  21  ) 

^    (  16-    5  )    , 

This  indicates  an  extreme  irregularity  in  the  number  of 
coils  in  each  circuit,  but  this  is  only  due  to  the  small  num- 
ber of  coils  necessarily  used  in  the  diagram.  In  any  wind- 
ing as  actually  used  the  irregularity  would  be  almost 
inappreciable. 


Fig.  1180. 
3176.     Fig.  1180  is  a  diagram  of  a  four-pole  two-circuit 
double-wound  armature  of  the  same  type  as  that  illustrated 


2010  APPLIED   ELECTRICITY. 

in  Fig.  1167.  For  this  type  of  two-circuit  ring  winding, 
formula  487  is  used;  but  to  obtain  an  even  distribution  of 
potentials  around  the  coramutator  only  the  —sign  should  be 
employed;  i.  e.,  s=p j  —  in.  In  this  case j=  11;  hence, 
J-  —  22  —  2  =  20.  As  y  and  in  are  in  this  case  also  mutually 
prime,  the  winding  forms  a  single  reentrant  system.  As  in 
Fig.  1179,  the  coils  are  numbered  i,  2,  3,  etc.,  and  the  num- 
bers 1',  2\  3',  etc.,  show  the  succession  in  which  the  coils 
are  connected.  Coils  1,  12,  and  3,  and  their  connections,  are 
drawn  in  heavier  lines  than  the  rest,  to  better  show  the  plan 
of  connection. 

Although  this  is  a  double  winding,  the  brushes  must  be 
made  of  a  span  equal  to  at  least  that  of  3  segments,  as  shown, 
in  order  that  they  may  be  in  connection  with  both  Avindings 
all  the  time.  This  width  is  necessary  because  each  coil  is 
connected  to  two  adjacent  segments. 

In  the  position  shown,  the  -fbrush  short-circuits  coils  1 
and  11,  and  the —brush  short-circuits  coils  16  and  6;  the 
direction  of  the  current  in  the  remaining  coils  is  indicated 
by  the  arrow-heads,  as  before.  The  four  circuits  of  this 
armature  are  made  up  as  follows,  starting  from  the  —brush: 


'  j  17-8-19-10  )   ~ 
(15-4-13-    2  f 
j  7  -  18  -    9  -  20  I 
I  0  — 


14  _    3-12  f 

This  winding  is  much  more  regular  than  that  shown  in 
the  previous  figure,  but  this  is  not  an  essential  feature  of 
this  form  of  winding,  being  due  to  the  even  number  of  coils 
and  windings. 

3177.  In  case  it  is  desired  to  make  the  cross-connec- 
tions a  part  of  the  commutator  construction,  which  is  usually 
more  desirable,  the  angular  span  of  the  cross-connections 
should  be  the  same  throughout,  in  order  that  the  cross- 
connections  may  be  symmetrical. 

With  the  winding  as  shown,  this  is  not  the  case,  for  the 
leading  segment  of  coil  1  is  connected  to  the  lO^A  segment 


APPLIED   ELECTRICITY.  2011 

to  the  right,  while  the  following  segment  of  the  same  coil  is 
connected  to  the  21st  segment,  also  to  the  right. 

If,  instead  of  connecting  the  two  ends  of  each  coil  to  ad- 
jacent segments,  they  are  connected  to  two  segments  which 
are  separated  by  a  third,  the  inequality  in  the  spans  of  the 
cross-connections  disappears,  and  they  become  symmetrical. 
This,  however,  causes  the  leads  from  the  armature  coils  to 
the  commutator  segments  to  cross,  requiring  extra  pre- 
cautions in  insulating. 

In  case  the  winding  were  triple,  quadruple,  etc.,  the  two 
ends  of  each  coil  would  be  connected  to  two  segments  sepa- 
rated by  2,  3,  etc.,  others;  that  is,  in  general,  the  two  com- 
mutator segments  to  which  each  coil  of  the  in  windings  is 
connected  would  be  separated  by  ni  —  1  other  segments,  if 
it  be  desired  to  make  the  cross-connections  a  part  of  the 
commutator  construction. 


MULTIPLE- W^OUND  MULTIPLE-CIRCUIT  DRUM  "WIIVDIIVGS. 

3178.  The  conditions  governing  the  multiple-circuit 
multiple-wound  ring  windings  also  apply  to  this  class;  in 
addition,  the  influence  of  the  difference  between  the  ring 
and  the  drum  form  of  coil  must  be  taken  into  account.  As 
each  coil  of  the  drum  winding  is  made  up  of  two  active 
parts,  each  occupying  a  winding  space,  the  number  of 
winding  spaces,  w,  must  be  even. 

The  back  pitch,  which  determines  the  number  of  winding 
spaces  included  between  the  two  active  parts  of  a  coil  (see 
Art.  3139),  needs  only  to  be  made  of  such  value  that  the 
two  parts  of  the  coil  shall  not  be  in  any  one  field  at  the 
same  time,  which  implies  that  the  angular  span  of  the  coil 

should  not  be  much  greater  or  less  than  -^r—» 

Zp 

The  front  pitch,  which  determines  the  numbei:  of  winding 

spaces  included   between   similar  parts    of   two   successive 

coils,  is  determined  by  the  number  of  separate    windings 

used.     In  the  multiple-circuit  single-ivound  drum  winding, 

the  front  pitch  =  back  pitch  ±  2;  that  is,  a  winding  space, 

belonging   to    another    part    of    the    winding,    intervenes 

between  the  adjacent  parts  of  successive  coils. 


2012  APPLIED   ELECTRICITY. 

In  the  multiple  windings,  in  addition  to  the  winding 
space  for  another  coil  of  the  same  winding,  there  must  also 
be  included  between  the  adjacent  parts  of  successive  coils 
two  winding  spaces  for  each  of  the  other  windings.  Conse- 
quently, the  difference  between  the  front  and  back  pitches 
must  be  2  in.  In  practice,  the  front  pitch  is  made  less  than 
the  back  pitch  for  reasons  already  given.  (Art.  3145.) 
Both  pitches  must  be  odd,  and  the  front  pitch  must  be 
opposite  in  direction  to  the  back  pitch. 

3179.  As  in  the  multiple-circuit  multiple- wound  ring 
windings,  the  number  of  separate  reentrant  systems 
formed  by  the  windings  will  equal  the  greatest  common 
factor  of  the  number  of  coils  and  the  number  of  windings; 
the  number  of  coils  being  equal  to  one-half  the  number  of 
winding  spaces,  the  number  of  reentrant  systems  is  equal 

"IV 

to  the   greatest   common  factor   of  —  and    in.     Any   even 

2 

number  of  winding  spaces  may  be  used,  whatever  the 
number  of  poles. 

In  order  to  prevent  opposing  E.  M.  F.'s  in  a  coil,  the 
number  of  winding  spaces  should  be  about  equal  to  the 
product  of  the  number  of  poles  and  the  average  of  the  front 
and  back  pitches.  (Compare  Art.  3156.)  It  is  usually 
rather  better  to  make  the  number  of  winding  spaces  a  little 
greater  than  this  product,  as  in  this  case  the  end  connec- 
tions are  a  little  shorter. 

31 80.  Fig.  1181  shows  a  diagram  of  a  four-pole  mul- 
tiple-circuit double-wound  drum  armature  having  20  coils 
(w  =  40).      The  back  pitch  is  taken  as  +13 ;  hence,  the  front 

zv 
pitch  =  -(13  -  2  in)  =  -  (13  -  4)  =  -  9.      y  (20)  being  a 

multiple  of  in  (2),  this  gives  two  separate  reentrant  systems. 
A  single  conductor  is  represented  in  each  winding  space, 
numbered  i,  2,  3,  etc. ;  the  order  in  which  the  conductors 
making  up  the  first  of  the  two  windings  are  connected  is 
indicated  by  the  numbers  i',  2  ',  3',  etc.,  and  the  order  of 
connection  of  the  conductors  of  the  second  winding  is  indi- 


APPLIED   ELECTRICITY.  2013 

cated  by  the  numbers  1" ,  2",  8",  etc.      Each   brush   short- 
circuits    a    single  coil,  and   the    short-circuited    conductors 


Fig.  1181. 


2,  9,  12,  19,  22,  29,  32,  and  89  are  indicated  by  the  absence 
of  the  arrow-heads,  which  on  the  rest  of  the  conductors 
indicate  the  direction  of  the  current  in  them. 


MULTIPLE-TV^OUIVD   TTI^O-CIRCUIT  DRUM   WINDINGS. 

3181.  The  principles  and  formulas  given  for  two-cir- 
cuit single-wound  drum  windings  require  only  slight  modi- 
fications to  adapt  them  to  this  class  of  windings. 

The  front  and  the  back  pitches  being  in  the  same  direction 
may  be  alike  or  may  differ  by  2.  In  either  case,  each  pitch 
must  be  odd ;  so,  if  both  pitches  are  alike,  the  average  pitch 


2014  APPLIED  ELECTRICITY. 

must  be  odd,  but  if  they  differ  by  2,  the  average  pitch  may 
be  even. 

In  the  single-wound  two-circuit  drum  winding  it  was 
pointed  out  that,  in  passing  through  the  winding,  the  second 
winding  space  to  one  side  or  the  other  of  that  at  which  the 
start  was  made  would  be  arrived  at  after  passing  under  each 
pole  in  succession,  and  from  this  the  formula  given  for  the 
number  of  winding  spaces  was  derived. 

In  the  multiple-wound  two-circuit  drum  windings,  in  ad- 
dition to  this  one  winding  space  belonging  to  the  sa7n^ 
winding,  two  others  for  each  of  the  other  windings  of  the 
armature  must  also  intervene  between  the  winding  space 
started  with  and  that  passed  through  after  making  one 
series  of  steps  around  the  armature.  From  this  it  follows 
that  the  total  number  of  winding  spaces  allowable  will  be 
given  by  the  formula 

w  =  2p  y  ±2m,        (488.) 

y  being  the  average  pitch,  and/  and  in  being  the  number  of 
pairs  of  poles  and  the  number  of  windings,  respectively,  as 
before.  As  in  all  two-circuit  windings,  only  two  brushes 
are  necessary,  although  two  for  each  pair  of  poles  may  be 
used  if  desired. 

The  number  of  separate  reentrant  systems  formed  will 
be  equal  to  the  greatest  common  factor  of  m  (the  number 
of  windings)  andy  (the  average  pitch). 

3182.  In  Fig.  1183  is  shown  a  diagram  of  a  four-pole, 
double-wound,  two-circuit  drum  armature,  having  the  same 
number  of  coils  (20)  as  the  multiple-circuit  armature  illus- 
trated in  Fig.  1181.  In  this  case  the  pitch,  both  front  and 
back,  is  taken  as  9,  and  the  number  of  winding  spaces 
found  from  formula  488,  as  follows: 

w  =  2/ J  ±  2  w  =  36  ±  4  =  40  or  32. 

In  this  case  40  winding  spaces  was  the  nvimber  used.  As 
before,  one  conductor  in  each  winding  space  is  represented, 
they  being  numbered  1,  2,  3,  etc.  Since  the  greatest  com- 
mon factor  oi  y  (9)  and  m  (2)  is  1,  this  winding  results  in  a 


APPLIED   ELECTRICITY. 


2015 


single  reentrant  system,  the  order  in  which  the  conductors 
are  connected  being  indicated  by  the  numbers  i',  2',  3',  etc. 
Two  brushes  are  shown,  the  +brush  short-circuiting  the 
coils  formed  from  conductors  13,  22,  31,  and  40,  and  the 
—  brush  short-circuiting  the  coils  formed  from  conductors  3, 
12,  21,  and  30,  these  being  indicated  by  the  absence  of  the 


Fig.  1182. 
arrows  which,  with  the  other  conductors,  indicate  the  direc- 
tion of    the   current    in  them.      The  path   of   the   current 
through  the  four  circuits  of  this  armature,  starting  from  the 
—  brush,  is  as  follows: 

j     1-10-19-28-37-   6-15-24-33-2  ) 
■j  32-23-14-  5-3G-27-18-  9  ) 

j  39-   8-17-26-35-   4  ) 

1  34-25-16-  7-38-29-20-11  ) 


+ 


2016  APPLIED   ELECTRICITY. 

It  will  be  seen  that  some  irregularity  is  indicated,. owing 
to  the  coils  short-circuited  by  the  —brush  being  taken 
wholly  from  the  second  winding.  With  the  necessarily 
large  number  of  conductors  used  in  practice,  the  difference 
between  the  number  of  conductors  in  the  different  branches 
of  the  winding  forms  such  a  small  percentage  of  the  whole 
number  employed  as  to  make  its  effect  negligible. 

3183.  One  of  the  principal  advantages  of  multiple 
winding  as  applied  to  drum  armatures  appears  when  bar 
windings  (a  single  conductor  per  winding  space,  with  sepa- 
rate end  connections)  are  used. 

In  this  form  of  winding,  the  bars  are  usually  set  in  slots 
cut  in  the  periphery  of  the  armature  core,  and  it  is  very  de- 
sirable that  the  number  of  slots  adopted  for  any  particular 
size  of  armature  be  such  that  they  may  be  used  for  windings 
giving  different  voltages,  without  change.  Thus,  for  exam- 
ple, of  the  two  windings  illustrated  in  Figs.  1181  and  1182, 
the  two-circuit  winding  (Fig.  1182)  will  evidently  give  twice 
the  E.  M.  F.  that  the  multiple-circuit  winding  (Fig.  1181) 
will  with  the  same  number  of  revolutions  and  in  a  magnetic 
field  of  the  sam.e.  strength,  the  only  change  made  in  the 
winding  being  in  the  span  and  arrangement  of  the  end  con- 
nectors. The  same  result  may  be  attained  by  changing  the 
multiple-circuit  winding  from  a  multiple-wound  to  a  single- 
wound  armature,  which  would  be  accomplished  in  this  case 
(Fig.  1181)  by  reducing  the  back  pitch  to  11,  or  increasing 
the  front  pitch  to  —11.  The  two-circuit  winding  can  not 
be  so  changed,  however,  in  a  four-pole  machine,  as  an  odd 
number  of  coils  is  required  for  the  single  winding  (Art. 
3165);  but  when  the  number  of  pairs  of  poles  is  odd,  as  in 
a  six-pole  machine,  an  even  number  of  coils  may  be  em- 
ployed for  the  single  winding,  and  this  may  be  changed  to  a 
double  winding  by  changing  the  end  connections,  if  desired, 
and  the  features  of  the  two-circuit  winding  retained. 

3184.  For  example;  suppose  that,  having  decided  on 
a  certain  number  of  revolutions  and  a  certain  number  of 
lines  of  force  in  the  field,  it  is  found  that  358  conductors  are 


APPLIED   ELECTRICITY.  3017 

required  for  a  six-pole,  single-wound,  two-circuit,  bar-wound 
drum  armature,  to  give  500  volts. 

From  formula  484,  w  =  2/j±2,  the  required  pitch 
may  be  found;  since  zv=.  358  and  /  =  3,  358  =  6  X  J  ±  3, 
from  which  y  =  ^^  =  59.3  +  or  ^^  =  60,  which  latter  value 
would  necessarily  be  used,  fractional  pitches  being  an  ab- 
surdity. As  the  front  and  back  pitches  must  each  be  odd, 
to  have  the  average  pitch  60,  the  front  and  back  pitches  may 
be  59  and  61,  respectively. 

In  case  it  was  desired  to  use  the  same  armature  for  a  250- 
volt  machine,  the  same  number  of  conductors  might  be 
used,  by  so  changing  the  pitch  as  to  make  a  double  winding. 
The  proper  pitch  to  use  would  be  found  from  formula  488, 
■w  =  2  p  y  ±  2  7u;  zv  =  358  as  before,  /  =  3,  and  7U  =  2,  and 
358  =  6  X/±  4;  hence,  j  =  3|_4  =  59^  or  -^  =  60.33+. 
59  would  be  taken  as  both  front  and  back  pitch.  It  would 
thus  be  only  necessary  to  slightly  change  the  end  connect- 
ors for  the  l>ack  pitch,  to  use  the  same  armature  for  either  a 
250-volt  or  a  500-volt  machine. 


THE  MAGNETIC  CIRCUIT. 

3185.  As  far  as  the  generation  of  the  E.  M.  F.  of  the 
dynamo  is  concerned,  it  is  only  essential  that  the  lines  of 
force  of  the  magnetic  field  be  present  at  the  points  where 
they  are  cut  by  the  conductors,  and  have  the  proper  direc- 
tion and  distribution.  However,  since  each  line  of  force  is 
continuous,  forming  a  closed  circuit,  provision  must  be 
made  for  a  complete  path  for  the  lines  of  force  to  and  from 
the  points  where  they  are  cut  by  the  conductors,  and 
through  the  magnetizing  coil  or  coils  wherein  they  are  gen- 
erated.  Of  course,  they  might  be  left  to  find  their  own  cir- 
cuit through  the  surrounding  air,  but  in  order  to  realize  the 
large  number  of  lines  of  force  required  with  the  expenditure 
of  a  reasonable  amount  of  magnetizing  force,  it  is  necessary 
that  the  path  of  the  lines  of  force  be  of  as  great  a  perme- 
ability as  possible;  i.  e.,  through  an  iron  or  steel  magjietic 
circuit. 


2018  APPLIED   ELECTRICITY. 

In  addition  to  the  armature  and  its  winding,  a  bipolar  or 
multipolar  dynamo  must  then  have  an  iron  or  steel  frame, 
or  Jield-jnagiiet,  which,  completes  the  magnetic  circuit  out- 
side the  armature.  This  frame  is  made  up  of  one  or  more 
pairs  of  pole-pieces,  from  (or  into)  which  the  lines  of  force 
pass  to  (or  from)  the  armature  through  the  spaces  between 
the  faces  of  the  pole-pieces  and  the  surface  of  the  armature 
core,  which  are  called  the  air-gaps ;  it  must  also  have  a 
part  upon  which  the  magnetising  eoils  are  wovmd,  which 
part  is  called  the  field  core.  The  part  of  the  frame  that 
joins  together  the  field  cores,  if  more  than  one  is  used,  or 
that  joins  the  pole-pieces  and  the  field  cores,  is  called  the 
magnetic  yoke. 


CONSTRUCTION    OF    FRAME. 

3186.  It  will  be  seen  that  the  object  of  the  frame,  as  a 
whole,  is  to  so  guide  the  lines  of  force  that  are  generated  by 
the  current  in  the  magnetizing  coils  that  they  will  enter  and 
leave  the  armature  at  the  proper  points,  forming  the  mag- 
netic field  in  the  air-gaps  of  the  required  distribution  and 
density. 

It  is  not  essential  to  the  operation  of  the  machine  that  the 
frame  be  of  any  given  form  or  size,  so  long  as  the  lines  of 
force  are  properly  delivered  to  the  armature;  economy  in 
materials  or  labor,  mechanical  strength,  and  other  consider- 
ations determine  the  form  and  size  of  frame  to  be  adopted. 

3187.  Since  the  magnetic  circuit  may  be  considered 
analogous  to  the  electric  circuit,  it  will  be  seen  that  in  order 
to  obtain  a  large  number  of  lines  of  force  with  a  moderate 
magnetizing  force,  the  reluctance  of  the  circuit  must  be 
low;  that  is,  the  iron  should  be  of  considerable  cross-section 
and  the  circuit  of  mioderate  length.  It  should  be  remem- 
bered that,  since  the  permeability  of  the  best  of  iron  is  only, 
perhaps,  1,500  times  that  of  air,  a  considerable  number  of 
lines  of  force  that  pass  through  the  magnetizing  coil  com- 
plete their  circuit  around  through  the  air  without  passing 


APPLIED   ELECTRICITY.  2019 

through  the  air-gaps.  To  reduce  this  magnetic  leakage  as 
far  as  possible,  surfaces  between  which  there  is  a  great 
difference  of  magnetic  potential  should  be  kept  as  far  apart 
as  the  design  of  the  magnet  will  allow,  and  made  of  as  small 
area  as  possible.  In  any  case,  some  ~  leakage  is  bound  to 
occur,  and  this  must  be  provided  for  by  making  those 
parts  of  the  frame  through  which  the  leakage  lines  pass  of 
sufficient  area  for  both  the  useful  and  the  leakage  lines. 
The  conditions  which  govern  the  leakage  will  be  more  fully 
discussed  later;  in  general,  the  area  of  the  iron  in  the  frame 
must  be  sufficient  for  from  15  to  50^  more  lines  of  force  than 
are  used  in  the  armature. 


DENSITY   OF  LINES  OF  FORCE. 

3188.  Referring  to  Fig.  952,  it  will  be  seen  that  the 
saturation  curves  there  shown  all  rise  in  a  nearly  straight 
line  for  some  distance  from  0,  then  curve  away  from  the 
axis  of  the  ordinates  and  follow  another  approximately 
straight  line,  which  makes  a  much  greater  angle  with  the 
axis  of  the  ordinates  than  does  the  first-mentioned  line. 
This  effect  is  much  more  marked  in  the  case  of  wrought 
iron  and  cast  steel  than  with  cast  iron,  but  in  any  case  it 
will  be  seen  from  this  feature  of  the  saturation  curves  that 
the  most  economical  density  at  which  to  work  the  iron  of 
the  magnetic  circuit  is  that  in  the  vicinity  of  the  bend  or 
"knee  "  of  the  curve.  A  much  lower  density  could  not  be 
economically  used,  because  a  considerable  increase  in  the 
number  of  lines  of  force  could  be  obtained  with  comparatively 
little  increase  in  the  magnetizing  force  required ;  and  on  this 
account  accidental  small  changes  in  the  magnetizing  force 
would  produce  a  considerable  change  in  the  number  of  lines 
of  force,  so  that  the  magnetic  circuit  of  the  machine  would 
be  in  an  unstable  condition.  A  much  higher  density  would 
not  be  economical,  because  the  increase  in  the  number  of 
lines  of  force  could  be  obtained  only  by  a  very  considerable 
increase  in  the  magnetizing  force. 


2020  APPLIED   ELECTRICITY. 

3189.  Applying  these  statements  to  the  curves  given 
in  Fig.  952,  it  will  be  seen  that,  in  general,  cast  steel  and 
wrought-iron  forgings  should  be  worked  at  densities  of  be- 
tween 80,000  and  100,000  lines  of  force  per  square  inch, 
while  sheet  iron  may  be  worked  higher,  between  90,000  and 
110,000  lines  of  force  per  square  inch.  With  cast  iron,  the 
curves  being  flatter,  the  allowable  range  is  somewhat 
greater,  the  usual  range  in  practice  being  from  25,000  to 
50,000  lines  of  force  per  square  inch,  the  latter  value  being 
used  only  in  the  case  of  the  best  grades  of  soft,  gray  cast 
iron. 

The  best  densities  to  use  are,  therefore,  not  those  that 
give  the  maximum  permeability  of  the  iron  used,  as  at  that 
point  the  iron  would  be  in  the  unstable  condition  referred  to 
previously. 

31 90.  From  the  above  and  from  the  curves  referred  to, 
it  appears  that  for  the  same  expenditure  of  magnetizing 
force  a  cast-iron  magnetic  circuit  must  have  about  twice  the 
sectional  area  of  one  of  cast  steel  or  wrought  iron,  in  order 
to  realize  the  same  number  of  lines  of  force,  so  that  the  cast- 
iron  magnetic  circuit  would  be  about  twice  as  heavy  as  one 
of  steel  or  wrought  iron;  its  less  cost  per  pound,  however, 
may  often  counterbalance  this  extra  weight,  and,  in  fact, 
the  choice  of  materials  for  the  frame,  as  well  as  almost  all 
the  other  features  of  a  dynamo,  depends  upon  the  local  con- 
ditions governing  each  particular  case. 

3191.  The  density  used  in  the  air-gaps  varies,  but  the 
best  practice  fixes  it  at  somewhere  in  the  neighborhood  of 
30,000  lines  of  force  per  square  inch;  this  depends,  however, 
on  many  other  features  of  the  design,  as  will  be  pointed  out 
later. 

In  any  case,  the  amount  of  the  magnetizing  force  that  is 
required  to  force  the  magnetic  flux  through  the  air-gaps  is  a 
large  proportion  of  the  total  amount,  since  the  permeability 
of  the  air-gaps  is  1,  which  much  more  than  compensates  for 
their  comparatively  short  length. 


APPLIED   ELECTRICITY. 


2021 


FORM  OF  MAGNETIC  CIRCUIT. 

3192.  The  form  of  the  magnetic  circuit  is  subject  to 
many  variations;  there  are,  however,  two  general  classes 
into  which  they  may  all  be  divided.  In  the  first,  a  single 
source  of  magnetizing  force  for  each  pair  of  poles  (which 
may  reside  in  one  or  more  magnetizing  coils)  sends  the  lines 
of  force  around  through  a  magnetic  circuit,  of  which  the  air- 
gaps  and  armature  directly  form  a  part.  Such  an  arrange- 
ment is  said  to  have  salient  poles.  In  the  second  type, 
at  least  two  magnetizing  forces  are  necessary  for  each  pair 
of  poles;  these  magnetizing  forces  act  in  opposite  directions 
upon  a  complete  magnetic  circuit,  and  the  opposing  lines  of 
force  cause  consequent  poles  to  appear  at  points  on  the  mag- 
netic cfrcuit,  which  points  are  properly  provided  with  pole- 
pieces,  between  which  the  armature  is  located.  Such  an 
arrangement  is  said  to  have  consequent  poles. 

3193.  One  of  the  simplest  forms  of  salient-pole  bipolar 
field-magnets  is  represented  in  Fig.  1183.  In  this  form  the 
magnetizing  force  is  supplied  by  the 
single  coil  shown  in  section  at  W 
and  W.  '  This  surrounds  the  field 
core  C^  to  which  are  attached  the 
magnet  yokes  3f  and  Af,  which  termi- 
nate in  the  pole-pieces  iV  and  5.  Be- 
tween these  pole-pieces  the  armature 
A  revolves.  The  mean  paths  of  the 
lines  of  force  through  the  magnetic 
circuit  (neglecting  leakage  lines)  are  fig.  1183. 
indicated  by  the  dotted  lines  having  the  arrow-heads,  which 
indicate  the  direction  of  the  lines  of  force,  assuming  the 
polarities  of  the  pole-pieces  to  be  as  indicated  by  the  letters 
N  and  5".  In  this  figure  the  field  core  is  represented  as  being 
vertical,  and  this  type  of  magnet  is  so  used  in  certain  ma- 
chines of  English  make.  It  may,  however,  be  either  vertical 
or  horizontal,  and  be  above,  below,  or  on  either  side  of  the 
armature,  as  desired.  The  Jenney  motors,  the  Wood  bi- 
polar machines,  the  Holtzer-Cabot  small  motors,  and  others 


2022 


APPLIED   ELECTRICITY. 


made  in  this  country  use  this  type  of  magnets  with  the  coil 
horizontal  and  below  the  armature.  Further,  the  armature 
shaft  may  either  have  the  direction  indicated  or  be  at  right 
angles  to  that  direction,  if  desired,  without  changing  the 
character  of  the  field-magnet.  The  mechanical  construc- 
tion in  this  last  case  would  evidently  be  bad,  and,  in  general, 
this  is  the  principal  feature  which  determines  the  disposition 
of  the  magnet  frame  with  regard  to  the  armature. 


3194.     A  form  of  consequent-pole  field-magnet  which  is 
derived  from   that  just  described   is   shown   in   Fig.    1184. 

This  form  of   field-mag- 


net is  known  as  the 
"  Manchester  type,"  and 
is  used  by  the  Mather 
Electric  Co.,  the  West- 
inghouse  Co.,  and  others 
in  this  country. 

This  is  practically  the 
same  form  of  magnet  as 
Fig.  1184.  that  shown  in  Fig.  1183, 

with  the  addition  of  a  second  similar  magnet  situated  on  the 
opposite  side  of  the  armature  A,  as  indicated  by  the  letters 
N',  M\  C,  M\  and  S'. 

Assuming  that  the  same  total  number  of  lines  of  force 
passes  through  the  armature  in  each  case,  it  follows  that 
with  the  consequent-pole  magnet  (Fig.  1184)  each  half  of 
the  magnetic  circuit  contains  half  the  total  number  of  lines, 
and  needs,  therefore,  to  be  of  but  half  the  sectional  area  of 
the  frame  of  the  salient-pole  magnet,  which  carries  all  the 
lines  of  force,  as  is  indicated  by  the  relative  proportions  of 
the  two  magnets.  (See  Figs.  1183  and  1184.)  Conse- 
quently, the  weight  of  the  frame  in  either  case  is  about 
the  same. 


3195.  In  the  consequent-pole  magnet,  the  magnetic 
circuit  in  each  half  is  approximately  the  same  length  but  of 
half  the  area  as  that  of  the  salient-pole  magnet;  its  reluc- 


APPLIED  ELECTRICITY. 


2023 


tance  is  about  twice  as  great,  but  since  it  carries  half  the 
number  of  lines  of  force,  it  follows  that  the  magnetizing 
force  required  for  each  half  oi  the  consequent-pole  magnetic 
circuit  is  the  same  as  that  required  for  the  whole  of  the 
salient-pole  magnet.  However,  the  magnetizing  coils  on 
the  consequent-pole  magnet  are  of  smaller  diameter  than 
those  used  in  the  salient-pole  magnet,  so  that  the  weight  of 
copper  used  for  the  magnetizing  coils  of  the  former  type 
of  magnet  is  not  double  that  required  for  the  latter  type. 
The  actual  ratios  of  weights  of  copper  and  iron  may  be 
readily  calculated  for  any  particular  case,  but  there  are 
other  conditions  that  influence  the  choice  of  the  form  of 
magnet  to  be  used,  which  must  be  taken  into  account. 


3 1 96.  Fig.  1185  shows  the  adaptation  of  these  two  forms 
of  field-magnets  to  a  multipolar  machine.  In  the  figure, 
the  part  to  the  left 
of  the  vertical  diam- 
eter represents  the 
salient-pole  magnet, 
and  that  to  the  right 
represents  the  con- 
sequent-pole magnet, 
each  being  laid  out 
as  for  an  eight-pole 
magnet. 

The  salient  -  pole 
magnet  consists  of  a 
number  of  separate 
magnets,  each  with 
its  magnetizing  coil. 
It  is,  therefore,  nec- 
essary to  supply  some 
separate  support  for 
these  magnets.  In  the  consequent-pole  magnet,  however, 
the  whole  frame  is  continuous,  each  pole-piece  being  sup- 
ported by  a  field  core  on  each  side,  the  frame,  therefore, 
being  of  sufficient  mechanical  strength  for  its  own  support. 


Fig.  1185. 


2024 


APPLIED  ELECTRICITY. 


In  the  latter  form,  the  mean  length  of  the  magnetic  circuit 
for  each  pair  of  poles  is  less  than  with  the  salient-pole  mag- 
nets, which  results  in  a  slight  saving  in  magnetizing  force, 
other  things  being  equal. 

Of  the  above  types  of  magnets  for  multipolar  machines, 
the  salient-pole  type  is  used  in  the  "  Perrett  "  machines, 
built  by  the  Electron  Manufacturing  Co.,  and  the  con- 
sequent-pole type  is  used  by  the  Standard  Electric  Co.,  in 
this  country,  and  in  several  types  of  machines  made  abroad. 


3197.  The  two  simple  forms  of  field-magnets  which 
have  been  described  may  be.  considerably  modified  by 
changing  the  position  or  increasing  the  number  of  the  field 
coils.  For  example,  the  magnetizing  coil  of  the  salient-pole 
magnet  (Fig.  1183)  may  be  wound  over  the  entire  frame 
from  pole-piece  to  pole-piece,  as  in  the  "  ring-type  "  machine 
of  the  Mather  Electric  Co.  Similarly,  the  magnetizing  coil 
on  each  half  of  the  consequent-pole  magnet  (Fig.  1184)  may 
be  wound  over  the  entire  frame  from  pole-piece  to  pole- 
piece,  as  in  the  "  C  &  C  "  machines.  In  both  these  examples, 
the  field  cores  are  made  approximately  circular  in  outline. 

Further,  by  dividing  the  magnetizing  force  between  two 
coils,  and  locating  these  coils  in  the  part  indicated  as  the 

magnet  yoke  in  Fig.  1183 
(J/ and  J/),  a  type  of  field - 
magnet  results  which  is 
commonly  known  as  the 
horseshoe  type,  as  illus- 
trated in  Fig.  1186.  It  will 
be  seen  that  in  these  two 
forms  the  magnet  yoke  (M) 
of  each  corresponds  to  the 
field  core  of  the  other.  This 
Fig.  1186.  type  of  field-magnet  is  very 

extensively  used  for  bipolar  machines,  the  Thomson-Hous- 
ton, Crocker- Wheeler,  Connecticut,  Keystone,  and  other 
makes  of  machines  using  it  in  the  position  shown,  i.  e.,  with 
the  magnet  frame  beneath  the  armature. 


APPLIED   ELECTRICITY. 


2025 


The  General  Electric  Co.  in  their  Edison  machines,  the 
Commercial  Electric  Co.,  the  Eddy  Electric  Manufacturing 
Co.,  and  others,  use  the  same  form  of  magnet  in  the  reverse 
position,  i.  e. ,  with  the  magnet  frame  above  the  armature. 

The  Excelsior  arc  machine  employs  the  same  type  of 
magnet,  but  with  the  armature  shaft  parallel  to  the  field 
cores,  passing,  therefore,  directly  through  the  magnet  yoke. 
The  pole-pieces  are  necessarily  modified  in  shape  to  suit  the 
changed  position  of  the  armature,  and  are  extended  to 
embrace  three  sides  of  the  armature,  which  is  ring  wound. 


3198.  The  consequent-pole  magnet  that  results  from 
combining  two  horseshoe  magnets  of  the  types  illustrated  in 
Fig.  1186  is  shown  in  Fig.  1187. 
Here  the  various  letters  have  the 
same  reference  as  in  the  previous 
figures.  As  in  that  previously 
described,  the  consequent-pole  ar- 
rangement requires  only  half  the 
cross-section  of  metal  in  each  half 
of  the  magnetic  circuit,  but  the 
total  amount  used  is  about  the 
same.  This  is  also  a  commonly 
used  type  of  bipolar  field-magnet. 
Among  others,  it  is  used  in  the 
Wood  arc  machine  of  the  larger 
sizes,  in  the  position  represented  in 
the  figure,  i.  e.,  with  the  field  cores 
{C,  C,  C,  C)  vertical.  The  Weston 
and  the  Schuyler  arc  machines  use  fig.  US'? 

the  same  form  of  field-magnet,  but  with  the  field  cores 
horizontal,  and  it  has  also  been  used  in  this  same  position 
for  various  special  machines  built  by  the  General  Electric 
Co.  and  others. 

The  smaller  sizes  of  the  Wood  arc  machine  use  this  form 
of  magnet  with  the  field  cores  horizontal,  and  with  the  shape 
of  the  pole-pieces  modified  so  as  to  allow  of  the  armature 
shaft  being  parallel  to  the  field  cores,  it  passing  through  and 


2026 


APPLIED  ELECTRICITY. 


having  its  bearings  in  the  yokes  {MandM).  The  Brush  arc 
machine  uses  a  similar  construction,  but  the  armature  is  made 
in  the  form  of  a  ring-wound  disk,  and  the  pole  faces  face  the 
end  faces  of  the  armature,  as  represented  in  the  diagram.  Fig. 
1188.     The  magnet  in  this  case  might  be  considered  to  be  two 

separate    bipolar,    salient- 
pole,  horseshoe  magnets. 


•AVAwar 


VAVi 


|W/ftW.V.*4- 


ffi 


•••••••••• 


s^ 


WWAW 


AVMAVft 


^JWWWW 


3 1 99.  By  carrying  the 
magnetizing  coils  still  fur- 
ther along  the  frame,  until 
they  are  as  close  as  possi- 
ble to  the  ends  of  the  pole- 
pieces,  still  another  type 
of  field-magnet  results,  as 
represented  in  Fig  1189. 
As  shown,  this  is  a  very  heavy  and  clumsy  magnet,  requir-. 
ing  a  large  amount  of  material  on  account  of  the  length  of 
the  magnet  yoke,  MM.  If,  however,  half  the  material  in 
this  yoke  be  located  on  the  other  side  of  the  armature,  so 
that  the  magnetic  circuit  through  the  frame  from  field  core 
to  field  core  consists  of  two  branches,  a  much  neater  and 


FIG.  1188. 


Fig.  1189. 


lighter   magnetic   circuit,   that   is   quite    extensively    used, 
results,  as  represented  in  Fig.  1190. 

This  form  of  circuit  still  has  salient  poles,  since  the  poles 
are  produced  by  the  direct  action  of  the  magnetizing  forces,, 
and  not  by  the  opposition  of  two  magnetizing  forces. 


APPLIED   ELECTRICITY. 


3027 


M 


M 


It  has  the  advantage  that  the  magnetizing  coils  and 
armature  are  enclosed  by  the  frame,  thus  affording  them 

mechanical    protection. 

This  type  of  magnet 
is  used  (in  the  position 
shown)  by  the  makers 
of  the  "  Detroit  "  dyna- 
mos, by  the  Western 
Electric  Co.,  and  by 
others  in  this  country 
and  abroad. 

The  Thomson-Hous- 
ton arc-lighting  dyna-  fig.  ii90. 
mos  also  employ  this  type  of  field-magnet,  the  form  being 
modified  by  making  the  magnet  yokes  of  a  series  of  round, 
wrought-iron  bars,  which  connect  together  circular  flanges 
on  the  ends  of  the  field  cores,  thus  making  the  general 
outline  cylindrical. 

Eickemeyer  has  used  it  for  very  compact  machines  in 
which  the  magnetizing  coils  actually  enclose  the  armature, 
the  field  cores  being  very  short. 

The  same  form  of  magnet,  but  with  the  magnetizing  coils 
above  and  below  the  armature,  was  used  in  the  old  Hoch- 
hausen  dynamos,  also  by  the  Thomson-Houston  Company 
for  their  old  "  S.  R.  G."  railway  motors,  and  by  others. 


3200.     With  this  arrangement  of  the  magnetizing  coils, 
a  consequent-pole  bipolar  magnet  is  not  possible;  but  by 

reversing  one  of  the 
coils  so  that  the  two 
magnetomotive  forces 
are  opposite,  two  conse- 
quent poles  will  be  formed 
on  the  magnet  yokes  M 
and  M,  Fig.  1190,  at  a 
point  opposite  the  neu- 
tral spaces  of  the  bipolar 
Fig.  1191.  form;    and    by    locating 


2028 


APPLIED   ELECTRICITY. 


suitable  pole-pieces  at  these  points,  a  four-pole  magnet  results, 
as  represented  in  Fig.  1191.  It  will  be  seen  that  this  mag- 
net has  one  pair  of  salient  poles  N  and  N,  and  one  pair 
of  consequent  poles  5  and  vS.  This  gives  a  very  compact 
form  of  four-pole  magnet,  and  is  used  in  several  types 
of  railway  motors,  in  the  "Eddy"  slow-speed  stationary 
motors,  and  by  other  makers.  The  "Wenstrom"  dynamos 
also  employ  a  somewhat  modified  form  of  this  type  of  field- 
magnet,  the  magnet  yoke  being  barrel-shaped  and  com- 
pletely enclosing  the  magnetizing  coils  and  pole-pieces, 
spaces  being  left  in  the  sides  for  the  removal  of  the  armature. 


3201.  By  winding  magnetizing  coils  around  the  con- 
sequent poles  of  the  type  of  magnet  illustrated  in  Fig. 
1191,  they  become  salient  poles,  giving  still  another  type 
of  field-magnet,  illustrated  in  Fig.  1192.  The  same  letters 
of  reference  are  used  in  this  figure  as  in  the  previous  ones. 

This  is  a  very  useful  form  of 
field-magnet,  and  is  that  most 
generally  used  in  this  country 
for  multipolar  machines  of  any 
number  of  poles,  almost  every 
maker  using  it  for  multipolar 
generators  and  alternators. 

The     various    magnet     yokes 
form   a  complete   ring,  which  is 
often,    especially    when    six    or 
Fig.  1192.  ,      more  poles  are  used,  made  circu- 

lar in  outline.  A  modification  of  this  form  of  magnet  is 
used  by  the  Siemens  &  Halske  Company,  in  which  the  field 
cores  project  radially  outward  from  a  common  hub,  instead 
of  inward,  the  armature  revolving  outside  the  poles  of 
the  magnet. 

3202.  The  number  of  possible  forms  of  field-magnets 
is  very  great,  although  they  may  all  be  classed  as  either 
salient  or  consequent  pole  magnets,  or  combinations  of  the 
two.     Many  of  the  forms  of  magnets  which  have  been  and 


APPLIED  ELECTRICITY. 


2029 


are  used  seem  to  have  been  designed  merely  with  a  view  to 
getting  something  different  from  any  other  maker,  and 
considerations  of  economy  of  material  or  of  mechanical 
fitness,  which  should  prevail  in  the  selection  of  a  design, 
have  been  largely  neglected.  These  forms  described  are  the 
basis  of  the  designs  of  field-magnets  in  modern  construction. 


METHODS  OF  EXCITING  THE  FIELD. 

3203.  The  requisite  number  of  ampere-turns  for 
exciting  the  field  of  a  dynamo-electric  machine  may  be 
obtained  in  a  variety  of  ways.  In  the  first  place,  the  cur- 
rent which  flows  through  the  magnetizing  coils  may  come 
either  from  some  separate  external  source,  the  machine 
being  then  said  to  be  separately  excited,  or  it  may  be 
furnished  by  the  ar- 
mature of  the  machine 
itself,  it  being  then 
said  to  be  self- 
excited.  In  some 
cases  a  combination 
of  separate  and  self-ex- 
citation may  be  used. 
A  diagram  illustrating 
separate  excitation  is 
given  in  Fig.  1193. 
The  current  required 
is  in  this  case  supplied 
by  the  primary  or 
secondary   battery  B,  fig.  1193. 

although  another  dynamo  may  be  used,  if  desired.  In  order 
to  adjust  the  current  in  the  magnetizing  coils  to  the  proper 
value,  or  to  vary  it  if  necessary,  an  adjustable  resistance 
r  is  included  in  the  field  circuit. 

The  armature  has  no  connection  whatever  with  the  field 
circuit,  but  supplies  the  external  circuit,  Re^  directly. 

3204.    It  is  evident  that  with  self-excitation  a  small  or  a 
large  current  may  be  used  in  the  magnetizing  coils,  accord- 


2030 


APPLIED   ELECTRICITY. 


Ing  to  the  nature  of  the  source  of  the  current,  a  large  or  a 
small  number  of  turns  being  used  in  the  magnetizing  coils 
to  give  the  necessary  magnetizing  force. 

Alternators  are  usually  separately  excited,  since  the  cur- 
rent given  out  by  the  machine,  being  alternating,  can  not  be 
used  directly  for  the  purpose.  Separate  excitation  has  also 
the  advantage  that  variations  of  the  output  of  the  armature 
of  the  machine,  caused  by  changes  in  the  speed  or  of  the 
current,  do  not  directly  affect  the  field  excitation. 


SERIES    WINDING. 

3305.     There  are  three  general  methods  by  which  self- 
excitation  is  accomplished.      In  the  first,  the   whole  of  the 

current  flowing  through  the 
armature  also  flows  through 
the  magnetizing  coils;  such 
a  machine  is  said  to  be 
series  -wound,  from  the 
fact  that  the  armature  and 
magnetizing  coils  are  con- 
nected in  series.  This  ar- 
rangement is  represented  in 
the  diagram  shown  in  Fig. 
1194. 

With    this  arrangement, 
the  magnetizing  force  act- 
FiG.  1194.  ing  on  the  magnetic  circuit, 

consequently  the  number  of  lines  of  force  in  the  magnet, 
varies  with  the  current  which  the  machine  furnishes  to  the 
external  circuit;  therefore,  when  the  armature  is  running 
at  a  constant  speed,  the  E.  M.  F.  which  is  generated  in  it 
varies  as  the  current  varies,  though  not  necessarily  in  the 
same  proportion.  This  is  not  usually  desirable,  since  most 
applications  of  direct  current  require  that  either  the  E.M.F. 
or  the  current  be  maintained  approximately  constant. 

3206.     To  realize  either  of  the  above  conditions  in  a 
series-wound  dynamo,  it  is  necessary  to  adopt  some  method 


APPLIED   ELECTRICITY. 


2031 


of  regulation,  whereby  either  the  effect  of  variations  in  the 
current  on  the  magnetizing  force  of  the  field  may  be  neu- 
tralized or  the  effective  E.  M.  F.  of  the  armature  may  be 
altered  to  suit  the  conditions.  The  former  result  may  be 
obtained  by  placing  an  adjustable  resistance  in  parallel  with 
the  magnetizing  coil,  as  represented  in  Fig.  1195.  In  this 
diagram,  5  F  represents  the  magnetizing  coil,  or  series 
field,  and  R  is  the  adjustable  resistance,  connected  in 
parallel  with  the  magnetizing  coil,  as  described.     It  will  be 

SF 


Fig.  1195. 

seen  that  the  current  divides  between  the  two  branches  of 
this  part  of  the  circuit,  and  by  varying  the  resistance  R  the 
proportion  of  the  whole  current  that  flows  through  the 
magnetizing  coil  5i^may  be  varied  as  required. 

The  method  of  varying  the  effective  E.  M.  F.  that  is  used 
in  the  Thomson-Houston  open-coil  armature  has  already 
been  described  (Art.  3086).  Another  method  of  accom- 
plishing the  same  result  with  closed-coil  armatures  is  to 
shift  the  brushes  away  from  the  neutral  point,  which  entails 
special  construction  and  precautions  against  destructive 
sparking,  etc. 

3207.  Series  winding  is  very  little  employed  in  dyna- 
mos, except  for  machines  designed  to  give  a  constant  cur- 
rent, such  as  is  used  for  operating  lamps  or  other  devices 
that  are  connected  in  series.  For  motors,  however,  series 
winding  is  very  useful,  since  when  starting  up  under  heavy 
load,  or  whenever  taking  a  current  in  excess  of  the  normal 


2033 


APPLIED   ELECTRICITY. 


amount,  the  field  strength  is  increased,  which  increases  the. 
amount  of  the  reaction  between  the  armature  winding  and 
the  field,  that  is,  increases  the  turning  force  of  the 
armature.  

SHUNT    A^INDIXG. 

3208.  The  second  method  of  self-excitation  consists  of 
forming  a  separate  circuit  of  the  magnetizing  coils,  which 
are  connected  directly  between  the  brushes,  or  in  shunt  to 
the  external  circuit,  this  style  of  winding  being,  therefore, 
known  as  shunt  ^winding.  This  is  illustrated  in  Fig. 
1196.  It  will  be  seen  that  the  magnetizing-coil  circuit  is  in 
a  measure  independent  of  the  external  circuit  {Re),  it  being 
exposed  at  all  times  to  the  full  difference  of  potential  that 
exists  between  the  brushes  {-{-B  and  —B) ;  from  this  it 
follows  that  changes  in  the  current  flowing  in  the  external 
circuit  do  not  affect  the  magnetizing  force  acting  on  the 
field,  except  as  they  may  change  the  difference  of  potential 
between  the  brushes.  Changes  in  the  current  of  the 
external  circuit  do  affect  this  quantity  in  several  ways, 
namely,  by  varying  the  drop  due  to  the  resistance  of  the 


Fig.  1196. 


armature  winding,  by  varying  the  counter  inagnetomotive 
force  of  the  armature  winding,  and  by  varying  the  length 
of  the  path  of  the  lines  of  force  by  the  variations  in  the 
amount  by  which  they  are  distorted  by  the  cross  magneto- 


APPLIED   ELECTRICITY. 


2033 


motive  force.  (See  Arts.  3115  and  3118.)  This  last  is 
comparatively  unimportant,  but  the  other  two  require  care- 
ful consideration  in  the  design  of  dynamo  machinery,  as 
will  be  pointed  out. 

3209.  In  a  shunt-wound  motor  the  conditions  are  dif- 
ferent, the  magnetizing-coil  circuit  being  supplied  directly 
from  the  mains;  the  magnetomotive  force  then  depends 
simply  upon  the  difference  of  potential  between  the  supply 
mains,  which  is  usually  kept  constant,  so  that  in  general  a 
shunt-wound  motor  may  be  considered  to  have  a  constant 
magnetizing  force  acting  on  its  field-magnet. 


COMPOUND   IVIIVDING." 

3210.  From  the  above  statements  it  will  be  seen  that 
in  order  to  maintain  a  constant  difference  of  potential  be- 
tween the  brushes  of  a  dynamo  (assuming  a  constant  speed), 
the  magnetomotive  force  of  the  magnetizing  coils  must  be 
increased  as  the  current  increases,  both  to  increase  the 
number  of  lines  of  force  so  as  to  increase  the  E.  M.-  F. 
generated,  and  to  make  up  for  the  counter  magnetomotive 
force  of  the  armature  winding.  One  way  to  accomplish 
this  result  is  to  place  an  adjustable  resistance  (r.  Fig. 
1196)  in  the  magnetizing-coil  circuit,  which  may  be  gradually 
cut  outvas  the  current  output  increases,  thus  reducing  the 
resistance  of  the  magnetizing- 
coil  circuit,  and  increasing 
thereby  the  current  flowing 
through  it.  This,  however, 
requires  personal  attention, 
automatic  devices  for  vary- 
ing the  resistance  not  being 
satisfactory,  and  in  case  the 
current  from  the  dynamo 
fluctuates  rapidly,  it  is  diffi- 
cult to  operate  the  resistance 
with  sufficient  rapidity.  Since 
the  amount  by  which  the  mag-  Pie  ^g^^ 


+r 


2034  APPLIED    ELECTRICITY. 

netomotlve  force  of  the  magnetizing  coils  must  be  varied 
is  closely  proportional  to  the  current  flowing,  which  follows 
from  the  nature  of  the  causes  which  require  the  variation, 
it  is  possible  to  obtain  the  required  variation  by  providing 
additional  magnetizing  coils  through  which  the  main  cur- 
rent passes.  This  is  known  as  compound  ^vinding,  and 
is  illustrated  in  Fig.  1197. 

321 1.  It  is  evident  that  this  is  a  combination  of  series 
and  shunt  winding,  the  shunt  winding  furnishing  a  constant 
magnetizing  force  and  the  series  winding  an  additional  mag- 
netizing force  which  is  proportional  to  the  current  output 
of  the  machine.  This  latter  winding  is  so  proportion'ed  that 
it  furnishes  the  proper  increase  in  the  magnetomotive  force, 
as  the  current  increases,  to  make  up  for  the  dropping  off  of 
the  difference  of  potential  between  the  brushes  that  would 
otherwise  occur.  For  certain  classes  of  work,  a  little  more 
than  this  amount  is  provided,  so  that  the  difference  of  po- , 
tential  between  the  brushes  rises  slightly  as  the  current  out- 
put increases.  In  such  a  case  the  machine  is  said  to  be 
over-compounded. 

3212.  Compound  winding  is  seldom  used  for  motors, 
as  either  a  series  or  a  shunt  winding  serves  for  almost  all  con- 
ditions of  operation.  Nevertheless,  for  application  to  such 
machinery  as  printing-presses,  a  compound  winding  is  ex- 
tremely useful,  as  the  series  turns  produce  a  powerful  field 
at  starting  and  at  slow  speed,  and  they  may  gradually  be 
cut  out  or  connected  in  various  combinations  to  produce 
different  working  speeds  without  the  necessity  of  inserting 
an  external  resistance  in  the  armature  circuit,  except  for 
starting  up,  when  a  resistance  may  be  temporarily  used. 


BUILDING   UP  THE  FIELD. 

3213.  Any  iron,  after  being  magnetized,  retains  a 
certain  amount  of  residual  magnetism,  so  that  there  will  be 
a  small  E.  M.  F.  generated  in  the  armature  winding  when 
the  armature  is  rotated  and  the   field  circuit  left  open;  this 


APPLIED   ELECTRICITY.  2035 

is  utilized  to  start  the  current  in  the  magnetizing  coils.  In 
the  case  of  a  shunt-wound  dynamo,  when  the  machine  is 
started  and  the  magnetizing-coil  circuit  closed,  the  small 
E.  M.  F.  generated  in  the  armature  by  the  residual  magnet- 
ism sends  a  small  current  through  the  magnetizing  coils, 
producing  a  small  magnetizing  force.  If  this  magnetizing 
force  tends  to  send  lines  of  force  through  the  magnetic  cir- 
cuit in  the  same  direction  as  the  residual  magnetism,  the 
number  of  lines  of  force  will  be  increased;  this  will  increase 
the  E.  M.  F.,  which  increases  the  current  in  the  magnet- 
izing coils,  and  still  further  increases  the  number  of  lines  of 
force  and  the  E.  M.  F.,  which  process  continues  until 
further  increase  in  the  magnetizing  force  results  in  so  little 
increase  in  the  number  of  lines  of  force  that  the  E.  M.  F. 
generated  becomes  steady,  the  windings  being  so  designed 
that  this  shall  be  the  E.  M.  F.  at  which  it  is  desired  to  run 
the  machine. 

It  will  be  seen  that  if  the  external  circuit  is  open,  all  of 
the  current  that  the  E.  M.  F.  (due  to  the  residual  magnet- 
ism) produces  flows  through  the  magnetizing  coils;  if,  how- 
ever, the  external  circuit  is  closed,  only  a  part  of  the  current 
flows  through  the  magnetizing  coils,  so  that  the  field  will 
"build  up  "  more  slowly  than  with  the  external  circuit  open, 
and,  in  fact,  will  not  build  up  at  all  if  the  external  resistance 
is  low  as  compared  with  the  armature  resistance.  From  this 
it  follows  that  a  shunt-wound  machine  should  be  started  up 
with  its  external  circuit  open. 

A  series-wound  machine,  on  the  contrary,  must  have  its 
external  circuit  closed  in  order  that  any  current  may  flow 
through  the  magnetizing  coils,  and  the  lower  the  resistance 
of  the  external  circuit  the  more  quickly  will  the  machine 
build  up. 

From  the  above  it  will  be  seen  that  a  compound-wound 
dynamo  may  be  started  with  its  external  circuit  either 
open  or  closed,  since  it  has  both  series  and  shunt  wound 
coils.  Usually,  however,  such  machines  are  started  and 
brought  to  their  full  E.  M.  F.  with  the  external  circuit 
open. 


3036  APPLIED   ELECTRICITY. 

3214.  At  starting,  while  the  current  is  increasing  in 
the  magnetizing-coil  circuit,  the  inductance  of  the  magnet- 
izing coils  increases  its  apparent  resistance,  and  a  part  of 
the  energy  supplied  to  the  coils  is  stored  up  in  the  magnetic 
field  which  is  being  established.  As  soon  as  the  current  in 
the  magnetizing  coils  reaches  its  maximum  value,  however, 
and  so  long  as  it  remains  constant  at  this  value,  there  is  no 
reactance  present,  and  the  entire  amount  of  energy  delivered 
to  the  coils  is  expended  in  heating  the  wire ;  that  is,  it  re- 
quires (directly)  no  energy  to  maintain  a  magnetic  field  at 
a  constant  value,  the  field  depending  on  the  ainpei'e-tiirns 
that  are  acting  on  the  magnetic  circuit.  It  is  obvious,  how- 
ever, that  in  order  to  force  the  current  through  the  wire  of 
which  the  magnetizing  coil  is  composed,  energy  must  be 
expended,  but  this  energy  appears  entirely  as  heat,  and,  con- 
sequently, is  wasted  as  far  as  any  practical  application  of  it 
is  concerned.  The  number  of  watts  expended  in  sending  the 
current  through  the  magnetizing  coils  should,  therefore,  be 
made  as  small  as  the  design  of  the  machine  will  permit,  both 
to  prevent  any  excessive  waste  of  energy  and  to  prevent 
possible  damage  by  the  heat  liberated.  In  practice,  the  loss 
of  energy  from  this  cause  varies  from  about  2  per  cent,  of 
the  total  output  of  the  machine  in  larger  sizes,  to  5  or  more 
per  cent,  in  the  smaller. 

3215.  In  shunt- wound  machines  the  magnetizing  coils 
are  exposed  to  the  full  difference  of  potential  that  exists  be- 
tween the  brushes  of  the  machine,  and,  consequently,  should 
use  only  a  small  amount  of  current  in  order  that  the  loss  in 
watts  should  be  the  required  small  percentage  of  the  output. 
From  this  it  follows  that  the  wire  used  for  the  magnetizing 
coils  should  be  of  small  size  and  of  considerable  length, 
making  a  large  number  of  turns  around  the  magnets,  both 
to  give  the  necessary  resistance  to  keep  the  current  at  its 
proper  value  and  to  allow  of  this  small  current  furnishing 
the  requisite  number  of  ampere-turns.  In  series-wound 
machines,  however,  as  the  total  current  flowing  gives  the 
magnetizing  force,  the  magnetizing  coils  need  to  have  com- 


APPLIED  ELECTRICITY,  2037 

paratively  few  turns,  which  should  be  of  correspondingly 
large  wire,  in  order  that  the  watts  loss  (which  is  equal  to 
C  R)  should  be  kept  within  the  desired  limits. 

It  will  be  seen  that  in  series-wound  dynamos  the  difference 
of  potential  between  the  terminals  of  the  machine  is  less 
than  that  which  appears  between  the  brushes  by  the  amount 
of  the  drop  in  the  magnetizing  coils. 

The  above  remarks  concerning  the  magnetizing  coils  of 
shunt  and  series  wound  dynamos  also  apply  to  those  of  com- 
pound-wound machiiies,  since  they  are  made  up  of  a  shunt 
and  a  series  winding. 


INDEX. 


Abscissas   .... 
Absolute  unit  of  potential 

"  units  . 

Acceleration,  Unit  of 
Accumulator     . 


"  cells,  Construction  of 

"  "      Method  of   set- 

ting up  . 
"  Chloride 

"  Discharge  rate  of 

"  Efficiency  of 

"  .  grids    . 

"  Internal  resistance  o 

"  Lead   . 

"   *         Phillips-Entz      . 
"  plants.  Failure's  of 

"  plates,  Life  of    . 

Accumulators,  Bimetallic 

"  Copper-zinc     . 

"  for  street  cars 

"  in  power  stations 

"  Installation  of 

"  Use  of 

Acid 

Acids,  Table  of 
Advance  of  winding 
Affinity,  Chemical    . 
Air-gap       .... 


Alternating  currents 

Alternator 

Amalgams  of  mercury     . 

Ammeter,  Edison  chemical 

"  Weston    . 

Ammeters 
Ammonium 
Ampere       .... 

"        and  coulomb.  Relation  be 
tween        .         .         .         , 


1674 


age. 

Page. 

1555 

Ampere-hour  efficiency  of  accumu- 

1586 

lator           .         .         .         . 

1768 

1474 

"        hours   

1765 

147s 

"        meters          .        .        .        . 

1634 

1746 

"        turns    

1543 

I7S9 

"            "      required  to  energize 

1770 

magnet  . 
Analogy   between    flow  of    water 

1573 

1793 

and  electricity        .         .         .         . 

1495 

177s 

Apparatus  for  measuring  current 

1629 

176s 

Area,  Unit  of 

1475 

1767 

Armature 

1518 

1770 

"            ...... 

1898 

1768 

"         core  losses 

1924 

1760 

"         reaction     .        .        .        . 

1969 

1778 

"          winding     .         .         .         . 

1898 

1797 

"          windings,  Closed-coil      . 

1973 

1770 

'•                   "           D  i  r  e  c  t -cur- 

1777 

rent     . 

1936 

1778   , 

"                  "          General  prin- 

1786 

ciples  of 

1929 

1786 

Armatures,  Closed-coil  bipolar 

1954 

1791 

"            Cylinder 

1935 

1781 

Disk       .         .         .         . 

1935 

1696 

"            Iron-clad 

1995 

1697 

"             Open-coil  bipolar 

1938 

1987 

"                       "        multipolar . 

1950 

1 701 

"             Unipolar 

1936 

1922 

Artificial  magnets    .        :        .        . 

1517 

2018 

Atomic  weights   of   chemical   ele- 

1927 

ments       

1695 

1928 

Atomicity  of  chemical  elements     . 

1695 

1694 

Available  electromotive  force 

1498 

1676 

Axis  of  magnetism  .         .         .         . 

1518 

B. 

Back  pitch  of  winding 
Bailie  and  Fery  cell 
Balance,  Torsion 
Ballistic  galvanometer 


Page. 


1750 
1453 


INDEX. 


Page. 


Ballistic     galvanometer    used     in 

measuring  magnetic 

qualities  of  iron 

Balloon  cell 

Bar  magnet 

"    winding 

Base  (chemical) 

Battery  connected  in  multiple  arc 

or  parallel 

"        connected   in  multiple   or 

parallel  series 
"        connected  in  series    . 
"        Electric 
"        Electrostatic 
"        Grouping  of  cells  of,    fo 

maximum  current . 
"        Le5fden 
"        Method  of  connecting  cell 

of       ...         . 
"        Primary 
"        Secondary  . 
"        Storage 
"        Voltaic 
Batteries,  Application  of 

Dry    .... 
Bichromate  cells 

Bimetallic  accumulators 

"  "  EflScienc 

of  . 
Binary  compounds  . 
Bipolar  armatures.  Closed-coil 

"  "  Open-coil 

"        drum  windings 
Bound  charge    . 
Bridge,  Wheatstone 
British  thermal  unit 
Broken  circuit  . 
Brushes 

Buckling  of  accumulator 
Building  up  field 
Bunsen's  cell 


C.  G.  S.  system  of  units  . 
Calculation  of  magnetic  circuit 
Calibration  of  galvanometer  . 
Callaud  cell 
Calorie 
Capacity     . 

"  Inductive  . 
Cardew  voltmeter  . 
Cathode 

Cell,  Bailie  and  Fery 
"     Bichromate 


Cell,  Bunsen 

"     Callaud 

I6II 

"     Chaperon  

1733 

"     Chemical  action  in  . 

1532 

"     Daniell 

IQ95 

"           "        crowfoot 

1697 

"     D'Arsonval       .... 

"     Edison-Lalande 

1472 

"     Fuller  bichromate  . 

"     Galvanic 

1472 

"     Gethin 

1472 

"     Globe  or  balloon 

1689 

"     Gonda-Leclanche     . 

1463 

"     Gouy  standard 

"     Gravity 

1757 

"     Grenet       

1689 

"     Grove         

"     Hercules 

1757 

"     Hussey      ..... 

1689 

"     Internal  resistance  of 

1689 

"     Kousmine           .... 

1689 

"     Lalande 

1466 

"     Latimer-Clark 

1752 

"     Leclanche          .... 

1751 

"  -  Little  Giant      .... 

1718 

"     Maeche 

1727 

"     Pabst 

1777 

"     Partz 

"     Poggendorf      .... 

1779 

"     Smee 

169s 

"     Sorley        .        .        .        .        . 

1954 

"     Voltaic 

1938 

"     Zinc-lead 

1982 

Cells,  Bichromate     .... 

1457 

"      Classification  of      .         .         . 

1638 

"      Grouping   of,  for  maximum 

1509 

current          .... 

1471 

"      Methods  of  connecting 

1930 

"      of  Volta  type 

1764 

"      with    depolarizing    electro- 

2034 

lytes  . 

1723 

"          "                  "               electro- 

lytes . 

Page. 

"          "       elementarysubstances 

1474 

applied  to  cathode  . 

1558 

"          "       elementarysubstances 

1600 

applied  to  cathode   . 

1734 

"          "       liquid  depolarizers     . 

1476 

"          "            "                 " 

1462 

"          "       non-depolarizing  elec- 

1458 

trolytes 

1677 

"          "       solid  depolarizers 

1700 

"          "           "               " 

1750 

"      without  depolarizers 

1718 

Centigrade  and  Fahrenheit  scales, 

1727 

Relations  between 

1649 


INDEX. 


Xlll 


Centimeter  .  .  .  .  . 
Chaperon  cell  ..... 
Character  of  commercial  currents 
Chardin's  arrangement  of  bichro- 
mate cells        .         . 

Charge,  Bound 

"        Free 

"        Negative      .        .        .        . 
"        Positive        .         .         .         . 
Charging    accumulators,    Precau- 
tions to  be  observed  in 
"  current  of  accumulator, 

E.  M.  F.  of   , 
Chemical  action         .... 
"  "      Electromotive 

f orceproduced  by 
Heat  formation  by 
in  galvanic  cell 
"  voltaic  cell 
Nature  of 
Weight    of    s  u  b  - 
stances  liberated 
by. 
affinity 
compounds 
elements   . 

Table  of 
equivalent 
formula    . 
nomenclature 
Chloride  accumulator 
Chord  winding 
Circuit 

"        Broken  . 
"        Closed   . 
"        Completed 
"        Divided 
"        External 
"        Grounded 
"        Internal 
"        Magnetic 
"        Open 

Shunt     . 
Circuits,  Magnetic 

"         Telegraph 
Closed  circuit    . 

"  coil  armature  windings 
"  "  bipolar  armatures 
"  "    winding 

Coefficient,  Temperature 
Coil-and-plunger  magnet 
"    Exciting     . 
"    Induction   . 
"    Primary 
"    Ruhmkorff 
"    Secondary 


Page. 
1474 
1743 
1927 

1721 
1457 
I4S7 
1451 
1451 

1794 
1769 


1705 
1704 
1 701 
1467 


1703 
1 701 


i6go 


169s 


1471 
1471 
1471 
1471 
1471 
1471 
1471 
1471 
2017 
1471 
1471 
1521 
1799 
147T 
1973 
1954 
i960 
1646 

1577 
1588 
1589 


Coils,  End  connections  of 
Collector    .... 
Combining  weight   . 
Commercial  efficiency  of  dynamo 
Commutation  of  current 
Commutator 
Compass     . 

"         Magnetic    . 
Compound  winding 

'*  wound  dynamo 

Compounds,  Chemical 
Condenser 
Conductivity 


"  Joint   . 

Conductors 

"  and  insulators,  Table  of    i 

Consequent  poles 


Conservation  of  energy 
Continuous  currents 
Controlling  magnet  of  galvanom 

eter  .... 
Copper-zinc  accumulators 
Core,  Field 
"      Lamination  of 
"      losses 
Coulomb     . 

"         and  ampere,  Relation  be 
tween 
Counter-magnetomotive  force 
Cross-magnetomotive  force    . 
Current  and  static  charge,  Differ^ 
ence  between  . 
"        Apparatus  for  measuring 
"        Commutation  of 
Effects  of    . 

"        Electric 

"        Graphical    representation 

of       ...        . 
"        in  conductors,  Effect  of 
"        strength.     Determination 
of,  by  decomposition  of 
water         .... 
"        strength  measured  by  cop- 
per deposit 
Currents,  Alternating 
"  Commercial 

"  Continuous 

"  Direct 

"         Pulsating 
"  Thermo-electric 

Curve,  Sine 
Curves,  Accuracy  of 

"        Method  of  plotting 


1930 
169s 
1909 
1962 
1931 
1532 
1518 
2033 
2033 
1690 
1461 

1455 
1500 
1501 
145s 


1522 
2021 
1508 
1927 

1599 
1778 
2018 
1925 
1924 
1480 

1480 
1972 
1972 


1962 
1478 
1591 
1463 

1911 
i9°5 


1631 

1631 
1927 
1927 
1927 
1927 
1927 
1470 
1917 
1557 
ISS7 


INDEX. 


Curves  of  magnetism 
'■  Permeability 
"        Saturation  . 

Cycle  of  magnetism 

Cyclic  alternating  E.  M.  F. 

Cylinder  armatures 
"  machines   . 

D. 

Daniell  cell 

"        crowfoot  cell 
D'Arsonval  cell 

"  galvanometer 

Dead-beat  instrument 
Decomposition,  Chemical 
Density,  Electric 

"  Magnetic    . 


"  of  lines  of  force 

Depolarization  .... 

"  Mechanical  devices 

for 
"  Rate  of     . 

Depolarizers       .... 

"  of   chlorides  of  me 

cury  and  silver 
"  "     oxides  of  lead 

"  "    sulphate   of   nier^ 

cury     . 
Depolarizing  effects  of  varioussub 

stances 

Derived  circuits,   Ohm's   law  ap 

plied  to 

Desiccator  .... 

Dielectric 

D'Infreville  ■wasteless  zinc     . 
Direct-current  armature  winding 

"       currents 
Direction  of  inducedcurrents,  Ruli 
for  . 
"         of  motion  of  conducto 
Rule  for 
Discharge  rate  of  accumulator 
Disk  armatures 
Divided  circuit 
Drop  of  potential 
Drum  winding  .... 
"      windings.  Multipolar    . 
Dry  batteries    .... 
Duncan  meter  .... 
Dynamo,  Compound-wound  . 
"         Over-compounded  . 
"         Self-excited 
"         Separately  excited  . 
"         Series-wound    . 
"         Shunt-wound    . 


Pag^e. 

1554 
'554 
1554 
1562 
1929 
1935 
1460 

Page. 

1735 
1730 
1606 

1673 
i6go 

1459 
1524 
1500 
2019 
1709 

1710 
1710 

1709 

1746 
1746 

1746 

1726 

1500 
1626 
1458 
1738 


Dynamo,  Theory  of 
Dynamometer,  Siemens  . 
Dyne 


1581 

1579 

1765 

1935 

1471 

1494 

1934 

1994' 

1751 

1681 

2033 

2034 

2029 

2029 

2031 

Z032 


E.  M.  F.,  Graphical  representation 

of 

"         in  closed-coil  armatures. 

Calculation  of 
"         of  charging  current 
"  "  the  formation  of  vari 

ous  sulphates     . 
"  "  zinc  with  various  elec 

trolytes 
Earth  (grounded)  circuit 
Earth's  magnetic  field,  Horizontal 

component  of  .         .         . 

Eddy  currents  .... 
Edison  chemical  ammeter 

"        Lalande  cell 
Efficiency  of  bimetallic  accumula 
tors 
"  Commercial     . 

"  Electrical 

"  of  dynamo 

Electric  battery 
"  current 
"  "        Unit  of  . 

"        density 

"        motor  .... 
"        pendulum    . 
"        quantity,  Unit  of 
"        series   .... 
Electrical  and  magnetic  units.  Re- 
lation between    . 
"         apparatus,  Description  of 


1674 
1476 


"  Experiments 

with    . 
"  Experiments 

with   . 
"  Experiments 

with   . 
"  Experiments 

with   . 
circuits   compared    with 
flow  of  water  through 
a  pipe 
efficiency  of  dynamo 
equivalent  of  heat  . 
horsepower 
instruments 
measurements.  Practical 
mechanical,  and  heat  en- 
ergy. Relations  of 
power        .        .        .        . 


1901 
1769 

1718 

1718 
1471 

1595 
1924 
1676 
1744 

1779 
1909 
1909 

1973 
1689 

1463 
1476 

1450 
1910 
1450 
1476 


152a 

1531 
1660 

1536 

1548 

1585 

1666 


1473 
1909 
1509 
1514 
1670 
1670 


INDEX. 


Electrical  resistance 
"  units 

"  work 

Electricity    and     flow     of     water 
Analogy  between 
"  Nature  of 

"  Static 

"  Voltaic    . 

Electrification  .... 
Electrochemical  calculations 
"  equivalent   . 

"  equivalents  . 

"  measurements 

"  theories 

Electrochemistry 
Electrodes  of  cell  or  battery  . 
Electrodynamics 


Electrolysis 
Electrolytes 


Page. 
1455 
1472 

1505 

1495 
1449 
1450 
1466 
1655 
1701 
1703 
1699 
1625 
1706 
1699 
1466 
1450 
1462 
1591 
1466 
1700 
164s 
1546 
1571 
1547 


"  Resistance  of 

Electromagnet  .... 
"  Calculation  of 

"  Horseshoe 

"  Iron-clad 

Electromagnetic  induction 

"  measurements 

"  reaction 

Electromagnetism    . 
Electromagnets,  Classes  of     . 
Electromotive  force 

"  force,  Available 

"  force,      Determina- 

tion of    . 
"  force,  Generation  of 

"  force   produced   by 

chemical      action, 
^  Calculation  of 

"  force,  Total 

"       Unit  of 
"  "       Value  of 

"  series 

Electrophorus   . 
Electropoion  fluid    . 
Electroscope 
Electrostatic  battery 
field     . 
"  induction 

"  instruments 

"  machines    . 

"  "  Cylinder 

"  "  Induction 

"  "  Plate 

Electrostatics 1450 

Elements,  Atomic  weight  of  .         .     i6gi 


1579 
1591 
1541 
1528 
1548 
15^8 


158s 


1705 
1498 
1476 
192 1 
1468 
1458 
1727 
1452 
1463 
1456 
1456 
1452 
1460 
1460 
1461 
1461 


Elements,  Chemical 
Table  of  . 
"  Voltaic     . 

End  connections  of  coils  . 
Energy,  Conservation  of 

"         equivalents,  Table  of 

"        Unit  of        .        .        . 

Equivalents,  Electrochemical 

Erg 


Exciting  the  Field,  Methods  of 
Experiments  with  electrical  appa 
ratus 
"  "     electrical  appa- 

ratus 
"  "     electrical  appa 

ratus 
"  "     electrical  appa- 

ratus 

"  "     electrical  appa- 

ratus. Sugges- 
tions for 
External  current 


Field,  Building  up  of 

"      core  .... 

"      Electrostatic  . 

"      Magnetic 

"      magnets.  Types  of 

"      Methods  of  exciting 
Force,  Electromotive 

"       Magnetizing  . 

"       Magnetomotive     . 
Unit  of   . 
Forming  accumulator  plates  . 
Frame  of  dynamo.  Construction 
Free  charge        .... 
Front  pitch  of  winding     . 
Fuller  bichromate  cell     . 
Fundamental  units  . 


Page. 


iggi 
1508 
IS" 
1476 
i6gg 
1703 
1476 
2029 

1536 


Q. 


Galvanic  cell 
Galvanometer 


Ballistic    . 

Calibration  of  .  1600 

constants  .        .  1600 

D'Arsonval      .         .  1606 

Reflecting        .         .  1605 

Sine  ....  1603 

Tangent  .         .         .  1597 

Theory  of         .        .  1592 

Generation  of  electromotive  force  1899 


1585 


1471 

Page. 
2034 
2018 
1456 
1519 
2028 
2029 
1468 
1550 
1543 
1476 
1772 
201S 
1457 
1983 
1728 
1474 

Page. 

1466 
1592 
1620 
1661 


XVI 


INDEX. 


Gethin  cell 

Globe  cell   .... 
Gonda-Leclanche  cell 
Gouy  standard  cell   . 

Gram 

Gi'.amme  winding 
Graphical  representation  of  E 

or  current 
Gravity  cell        .        . 
Grenet  cell 
Grid,  Reckenz.aiin     . 
Grids,  Accumulator 
Grounded  circuit 
Grounding  a  circuit 
Grove  cell  .... 


Page. 

1734 
1733 
1641 

1749 
1474 
1934 

1 911 
1734 
1719 
1774 
1770 
1471 
1653 
1723 


H. 

Halogens 

Harmonic  alternating  E.  M.  F. 
Heat  and  work,  Relation  between 

"     Equivalent  of  . 

"     formation  by  chemical  action 

"      Mechanical  equivalent  of 

"     of  formation     .... 

"      "  "         of   various  sub- 

stances     with 
oxygen     . 

"     Unit  of 

Hercules  cell 

Holtz  machine   ..... 
Horizontal   component   of  earth's 

field 

Horsepower,  Electrical    . 
Horseshoe  magnet    .... 

Hussey  cell 

Hydrate 

Hysteresis 


Power  expended  by 


1750 
1929 
1704 

1509 
1704 
1509 


1703 
1476 
1716 


1595 
1514 
1532 
17.34 
1696 
1562 
1924 
1564 


I.              -              Page. 
Induced  currents  in  closed  coil,  Di- 
rection of  .         .  1584 
"                "  -     Rule  for  direction 

of         .          .          .  1581 

"  .      E.  M.  P.,  Production  of    .  1587 

Induction-coil    ...         .         .         .  1589 

"          Electromagnetic      .         .  1579 

"         Electrostatic    .        .        .  1456 

"                       "■             machine    .  1461 

"         Magnetic           .        .        .  1524 

"          Mutual      ....  1588 

"         Self 1587 

"          Unipolar  ....  1936 

Inductive  capacity    ....  1458 

Input  of  dynamo       ,        .        .        .  1973 


Installation  of  accumulators 
Instruments,  Electrical    . 
"  Electrostatic 

"  Switchboard 

Insulation  .... 
",  resistance 

"  "  Measurement 

of 
"  resistance  of  apparatus 

for   electric-light  and 
power  work 
"  resistance  of  telegraph 

lines 


Page_ 
1791 
1670 
1452 
1682 
1649 
1649 

1655 


Insulators,. 


"  in  order  of  their  induct 

ive  capacity 
"  Resistances  of 

Internal  circuit 

"        resistance  of  accumulator 

"  "  cell 

"  "  "  voltaic  cell 

Iron-clad  armature  . 
"    Methods  of  testing  . 


1653 


1650 
1455 


1645 
1471 
1768 
1758 
1490 
1995 
1611 

J.  Page. 

Joint  resistance  of  conductors        .     1501 

Joule 1504 

Joule's  law 1509 

K.  Page. 

Keeper 1508 

Kilowatt 1516 

Kousmine  cell 1729 


Lalande  cell 
Lamination  of  core  . 
Latimer-Clark  cell   . 
Law,  Joule's 

"      Ohm's 

"      open-circuit  cell 
Laws  of  static  charges 
Lead  accumulators  . 
Leads 

Leakage,  Magnetic  . 
Leclanche  cell  . 
Leyden  battery 

"        jar 
Life  of  accumulator  plates 
Lifting  magnets 

"  "  Calculation  for 

Lines  of  force.  Density  of 

"       "        "      Magnetic . 

"        "        "      Rule  for  direction  o' 
Litharge 
Little  Giant  cell 


Page. 
1743 
1925 
1748 
'509 
1473 
1715 
1452 
1760 
i960 
1565 
1739 
1689 
1462 
1770 
1568 
1571 
2019 
1520 

■  1530 
174s 
1716 


INDEX. 


XVll 


Lodestone  . 
Long-range  magnets 
Loop  winding     . 


M. 

Machines,  Electrostatic   . 
Maeche  cell         .... 
Magnet  for  attraction      . 
"       calculation  for     . 
"        Coil-and-plunger 
"        Controlling 
Magnetic  and  electrical  units,  Re 
lation  between 
"         circuit 

"  "        Calculation  of 

"  "        Closed    . 

"  "        Compound    . 

"  "       Form  of 

"  "        Sectional  area   o 

"  "        Simple  . 

"  compass     . 

"  density 


Page. 

•  1517 

•  1577 

•  '995 

Page. 

1460 
1726 
1576 
1571 
1577 
1599 

1528 
1 52 1 
2017 
1558 
1523 
1523 
2021 

1523 
1522 
1518 
1524 
15S0 


Page. 


"  "        and  permeability 

of  iron  and  steel 
"         fields 
"         induction  . 
"         leakage 
"        lines  in  solenoid 
"  "      of  force     . 

"  "      per  unit  pole 

"         permeability     . 
"         poles,      Attraction      b  e 

tween 
"  "  Strength  of 

"         qualities   of   iron,   meas- 
ured  by   ballistic    gal 
vanometer 
"         satviration 
"        substances 
"         units  . 
"         yoke  . 
Magnetism 

"  Cj'cle  of 

"  Quantity  of 

"  Residual 

"  Unit  density  of 

Magnetite  . 

Magnetization,  Curves  o 
Magnetizing  force     . 
Magnetomotive  force 

"  "      Counter 

"  "      Cross    . 

"  "      Intensity   of 

Magnets,  Artificial  .        . 


1553 
1519 
1524 
1565 

1545 

1520 
1526 
1545 

1592 
1526 


i6ri 
1552 
1519 
1526 
2018 
1517 
1562 
1524 
1561 
1527 
I5'7 
1552 
1550 

1543 
1972 
1972 
1544 
1517 


Magnets,  Lifting 

"         Long-range 
"         Natural 
"  Permanent 

"  Short-range 

"         Tractive  force  of 
Mass,  Unit  of      .         .        . 
Maximum  current  of  battery 
Measurements,  Electrochemical 
"  Electromagnetic 

"  of  potential    . 

"  Precision  in    . 

"  with     commercial 

instruments 
Mechanical,  electrical,  and  heat  en 
ergy.  Relations  of 
"  equivalent  of  heat 

Megohm 

Metals,  Resistance  of 
Meter,  Duncan  . 

"       Shellenberger 
Microhm     . 
Minimum    . 
Multiple  arc,  Battery  connected  in 
"         circuit  windings 
"         windings     . 
"         wound  multiple-c  ircui 
drum  windings 
"  "       multiple-circuit 

ring  windings 
"  "       two-circuit    drum 

windings 
"  "       two-circuit    ring 

windings  . 
Multiplying  power  of  shunts  . 
Multipolar  armatures.  Open-coil 

"  drum  windings 

Mutual  induction 

N. 


1577 
1517 
1518 
1576 
1568 
1474 
1757 
1625 

1.59 1 
1632 
1623 

1682 


1509 
1483 


1483 

1745 
1472 

1977 
2002 


2007 
1621 
1950 
1994 
1588 


Negative  charge 
Neutral  line  of  magnet    . 

"        temperature 
Nitric  acid  as  a  depolarizing  liquid     1723 


Page. 

•  1451 
.  1518 
■     1470 


O.  Page. 

Ohm,  Legal        .         ....         .  1483 

"      Various  values  of  .         .         .  1482 
Ohm's  law          .         ;        .        .        .  1473 
"          "    applied   to    closed    cir- 
cuits       .  1491 
"         "           "        "     derived  cir- 
cuits       .  1500 
Open  circuit       ..        .         ...         .  1471 

'■  "       cell.  Law      .         .         .  1715 


XVlll 


INDEX. 


Page. 

Open-coil  bipolar  armatures  .        .  1938 

"          multipolar  armatures    .  1950 

"          •winding-    ....  1944 

Ordinates  ......  1555 

Output  of  dynamo    ....  1973 

Oxide  .......  i6qi 


Pabst  cell    . 
Parallax 

Parallel  or  multiple  arc,   Battery 
connected  in 
"  "  multiple  arc,    Conduc 

tors  connected  in 

Partz  cell 

Pendulum,  Electric 
Periodic  alternating  E.  M.  F. 
Permanent  inagnets 
Permeability   and   magnetic    den- 
sity   of    iron    and 
steel 
"  curves 

"  Magnetic  . 

Peroxide  of  lead  - 
Phillips-Entz  accumulator 
Pile,  Voltaic 
Pinnacle  zinc 
Pitch  of  winding 
Plate  electrostatic  machine 
Poggendorf  cell 
Polarity  of  solenoid  . 
Polarization 
Poles,  Consequent    . 

"      of  cell  or  battery  . 
"       "  magnet 
"       "  magnetic  compass 
"      Salient    . 
Positive  charge 
Potential     .... 
"  Absolute  unit  of 

"         Drop  of 
"         Measurement  of 
Power,  Electrical 

Unit  of  . 
Precision  in  ineasurements 
Primary  batteries,  Applicati 
"         battery 
"         coil 
Prime  conductor 
Pulsating  currents   . 

R. 

Rate  of  cutting  lines  of  force 
Reaction,  Armature 

"  Electromagnetic 

Reckenzaun  grid 


Page. 
1722 
1674 


on  of 


1472 

1471 
1728 
1450 
1929 
1518 


1553 
1554 
1545 
1745 
1778 
1469 

1737 
1978 
1461 
1720 
1542 
1709 
2021 
1466 
1518 
1518 
2021 
1451 


1494 
1632 

1476 
1623 
1752 


1460 
1927 

Page. 

•  1585 
.     1969 

•  1541 

•  1774 


Recomposition  (chemical) 
Reflecting  tangent  galvanometer 
Relations  of  mechanical,  electrical 
and  heat  energy 

"  "  thermometric  scales 

Reluctance 
Residual  magnetism 
Resistance 

"  coils 

"  "     Standard 

"  Electrical 

"  Insulation 

"  of  metals 

"  "  various    electrolytes 

"  "        "  insulators 

"  Specific  . 

Unit  of     .         .         . 
Reversal  method  of  testing  iron 
Revolution  counter  . 
Ruhmkorff  coil  .... 


Salient  poles 
Salt  (chemical)  . 
Saturation  curves     . 
"  Magnetic 

Secondary  battery    . 

"  cells 

"  coil  . 

"  units 

Self-induction  . 

Series,  Battery  connected  in 

"        Conductors  connected 

"        Electric 

"       Electromotive 

"        winding 

"       wound  dynamo 

Shellenberger  meter 

Short-range  magnets 

Shunt,  Galvanometer 

"       Multiplying  power  of 
"        winding 
"        wound  dynamo 
Siemens  dynamometer 

"  wattmeter. 

Sine  curve 

"    galvanometer 
Slide-wire  bridge 
Smee  cell    . 
Solenoid 

"         Magnetic  lines  in 
"         T'olarity  of 
Solution 
Sorley  cell 
Sparking  limit  . 


Page. 

1690 
1605 


1649 
1558 
1561 
1484 
1660 
1643 

1455 
1649 
1488 
164s 
164s 
1643 
1477 
1614 


Page. 

2021 
1697 
1534 
1552 
1689 
1746 


1475 
1587 
1472 
1472 
1452 
1468 
2030 
2031 
1681 
1576 
1620 
1621 
2032 
2032 
1674 
1678 
1917 
1603 
1660 
1714 
1542 
154s 
1542 
1697 
1774 
1972 


INDEX. 


Pag-e. 

Specific  resistance    ....  1643 

Standard  resistance  coils         .        .  1643 
Static  charge  and  current,  DifTer- 

ance  between       .         .         .  1468 
"      charges.  Laws  of  .         .         .  1452 
Statical  electricty.  Production  of  .  1450 
Step-by-step  method  of  testing  iron  1614 
Storage  batteries  (see  also  accumu- 
lators)      .        .  i68g 


"  "         Space      1 

for     . 
Switchboard  instruments 


1746 
1759 


I7Q2 

1682 


T.  Pag-e. 

Tachometers 1687 

Tangent  galvanometer    .        .        .  1597 
"                     "                 Reflecting  1605 
Telegraph  lines,  Insulation  resist- 
ance of     .....         .  1650 

Telephone  lines,  Insulation  resist- 
ance of     .....         •  1650 

Temperature  coefficient  .         .         .  1641 
"               coefficients  for  vari- 
ous metals       .        .  1647 
"               Neutral       .         .         .  1470 
Theory  of  the  galvanometer  .        .  1592 
Thermal  unit,  British       .         .         .  1509 
Thermochemical  equivalent  .         .  1702 
Thermoelectric  currents          .         .  1470 
Thermometric     scales.     Relations 
between  ......  1649 

Thomson  recording  wattmeter       .  1680 

Time,  Unit  of 1475 

Torsion  balance         .         .         .         .  1453 
"             "         Use  of    .        .        .  1454 
Total  electromotive  force        .        .  1498 
Tractive  force  of  magnet         .         .  1568 
"              "      "          "       how    cal- 
culated 1571 

Tudor  Grids 1773 

Two-circuit  windings       .         .         .  1976 

U.  Page. 

Unipolar  armatures          .         .         .  1936 

"         induction   ....  1936 

Unit  of  acceleration          .        .        .  1475 

"      "  area        .....  1475 

"      "  diiTerence  of  potential         .  1476 

"      "  electric-current  quality       .  1476 

"     "                 "              strength    .  1476 

"      "  electromotive  force     .         .  1476 

"     "  energy 1476 

"      "  force 1476 

"     "  heat 1476 


Unit  of  mass 

"      "  potential.  Absolute 
"      "  power     . 
"      "  resistance 
"      "  time 
"      "  velocity 
"      "  volume 
"      "  work 
Units,  Electrical 

"      Fundamental 

"      Magnetic 

"       Secondary 

V. 

Valency  of  chemical  eleinents 
Velocity,  Unit  of        .         .         . 

Volt 

Voltaic  battery 

cell         .... 

"  "     Internal  resistance  of 

"  "     Simplest  form  of 

"        couple   . 

"        electricity 

"        eleinents 

"        pile 
Volt-coulomb     . 
Voltmeter  . 

"  Cardew 

"  Weston 

Volume,  Unit  of 

W. 

Watt 

"      efficiency  of  accumulator 
Wattmeter,  Siemens 

"  Thomson  recording 

Wave  winding  .... 
Weston  ammeter  and  voltmeter 
Wheatstone  bridge  . 
Wimshurst  machine 
Winding,  Advance  of 

Bar     .... 
"         Chord 
"         Closed-coil 
"         Compound 
"  Drum 

"  Gramme 

■'         Loop  . 
"  Open-coil 

Pitch  of 
Ring  . 
"  Series 

"  Shunt 

"         Wave 
Windings,  Armature 

"  Bipolar  drum 


Page. 

1474 
1686 
1476 
1477 
M7S 
147s 
^475 
1476 
1472 
1474 
1526 
1475 

Page. 
1695 
147s 
1490 
1466 
1466 
1490 
1700 
1466 
1466 
1466 
1469 
1505 
1634 
1677 
1674 
1475 

Pag-e. 
1514 
1768 
1678 
1680 
1997 
1674 


1987 
1995 
1988 
i960 
2033 
1934 
1934 
199s 
1944 
1978 
1934 
2030 
2032 
1997 
1929 
1982 


XX 

IND 

Page. 

EX. 

Page. 

Windings,  Close 

id-coil 

1973 

Windings,  Multipolar  drum    . 

■     1994 

"           Direct-current 

1936 

Ring 

■     1974 

Mult: 

iple  .        .         .        . 

2002 

"           Two-circuit     . 

•     1976 

"                   " 

circuit 

1977 

Work  and  heat,  Relation  between     1704 

"                   " 

wound,  multi- 

"      Electrical 

•     1505 

ple-c  ire  u  i  t, 

"      Unit  of     ...        . 

■     1476 

drum     . 

2011 

" 

wound,  multi- 

Y. 

Page. 

ple-ci  r  cu  i  t, 

Yoke,  Magnetic 

.     2018 

ring 

2004 

"                   " 

wound,     two- 

Z. 

Page. 

circuit,  drum 

2013 

Zinc,  D'Infreville  wasteless    . 

■     1738 

" 

wound,      two- 

"      lead  accumulator  cell     . 

•     1777 

circuit,    ring 

2007 

"      Pinnacle    .... 

•     1737 

V5 


